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Solving a Fourth-Degree Equation in Excel

Author: kegasaExecutions: 816
TOP/Shared Formulas (Math)/General Math

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A formula that calculates the roots of a quartic equation just by copying it into an Excel cell
x1 = -1 * b2 / 4 + (sqrt(2 * (2 * sqrt(((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 *b2^2/8)^2/36)*cos(acos(((b3-3*b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/12 + ((b4 + b2^3/8 - b2*b3/2)^2 - 4*(b3 - 3*b2^2/8)*(b5 - b2*b4/4 + b2^2*b3/16 - 3*b2^4/256))/16 + (b3 - 3*b2^2/8)^3/216)/sqrt(-1*(-((b5 - b2*b4/4 + b2^2*b3/16 - 3*b2^4/256)/3) -(b3 - 3*b2^2/8)^2/36)^3))/3)+(b3 - 3*b2^2/8)/6)-(b3 - 3*b2^2/8))+sqrt(-(2*(2*sqrt(((b5 - b2*b4/4 + b2^2*b3/16 - 3*b2^4/256)/3) + (b3 - 3*b2^2/8)^2/36)*cos(acos(((b3 - 3*b2^2/8)*(b5 - b2 * b4/4 + b2^2 * b3/16 - 3 * b2^4/256)/12 + ((b4 + b2^3/8 - b2 * b3/2)^2 - 4 * (b3 - 3 * b2^2/8) *(b5 - b2 * b4/4 + b2^2 * b3/16 - 3 * b2^4/256))/16 + (b3 - 3 * b2^2/8)^3/216)/sqrt(-1 * (-((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) - (b3 - 3 * b2^2 / 8)^2 / 36)^3)) / 3) +(b3 - 3*b2^2/8)/6) + (b3 - 3*b2^2/8)) - 2*(b4 + b2^3/8 - b2*b3/2)/sqrt(2*(2*sqrt(((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 * b2^2 / 8)^2 / 36) * cos(acos(((b3 - 3 * b2^2 / 8) *(b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 12 + ((b4 + b2^3 / 8 - b2 * b3 / 2)^2 - 4 * (b3 - 3 *b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256))/16+(b3-3*b2^2/8)^3/216)/sqrt(-1*(-((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) -(b3 - 3*b2^2/8)^2/36)^3))/3) + (b3 - 3*b2^2/8)/6) - (b3 - 3*b2^2/8))))/2;
print(x1);

x2 = -1 * b2 / 4 + (sqrt(2 * (2 * sqrt((((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 *b2^2/8)^2/36))*cos(acos(((b3-3*b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/12 + ((b4 + b2^3/8 - b2*b3/2)^2 - 4*(b3 - 3*b2^2/8)*(b5 - b2*b4/4 + b2^2*b3/16 - 3*b2^4/256))/16+(b3-3*b2^2/8)^3/216)/sqrt((((b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/3)+(b3-3*b2^2/8)^2/36)^3))/3)+(b3-3*b2^2/8)/6)-(b3-3*b2^2/8))-sqrt(-(2*(2*sqrt((((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 * b2^2 / 8)^2 / 36)) * cos(acos(((b3 - 3 *b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/12+((b4+b2^3/8-b2*b3/2)^2-4*(b3-3*b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256))/16+(b3-3*b2^2/8)^3/216)/sqrt((((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 * b2^2 / 8)^2 / 36)^3)) / 3) + (b3 - 3 *b2^2/8)/6)+(b3-3*b2^2/8))-2*(b4+b2^3/8-b2*b3/2)/sqrt(2*(2*sqrt((((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 * b2^2 / 8)^2 / 36)) * cos(acos(((b3 - 3 *b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/12+((b4+b2^3/8-b2*b3/2)^2-4*(b3-3*b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256))/16+(b3 - 3*b2^2/8)^3/216)/sqrt((((b5 - b2*b4/4 + b2^2*b3/16 - 3*b2^4/256)/3)+(b3-3*b2^2/8)^2/36)^3))/3)+(b3-3*b2^2/8)/6)-(b3-3*b2^2/8))))/2;
print(x2);

x3 = -1 * b2 / 4 - (sqrt(2 * (2 * sqrt((((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 *b2^2/8)^2/36))*cos(acos(((b3-3*b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/12+((b4 + b2^3/8 - b2 * b3/2)^2 - 4 * (b3 - 3 * b2^2/8) * (b5 - b2 * b4/4 + b2^2 * b3/16 - 3 * b2^4/256)) /16 + (b3 - 3*b2^2/8)^3/216)/sqrt((((b5 - b2*b4/4 + b2^2*b3/16 - 3*b2^4/256)/3) + (b3 - 3*b2^2/8)^2/36)^3))/3)+(b3-3*b2^2/8)/6)-(b3-3*b2^2/8))+sqrt(-(2*(2*sqrt((((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 * b2^2 / 8)^2 / 36) * cos(acos(((b3 - 3 * b2^2 / 8)*(b5 - b2 * b4/4 + b2^2 * b3/16 - 3 * b2^4/256)/12 + ((b4 + b2^3/8 - b2 * b3/2)^2 - 4 * (b3 - 3 *b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256))/16+(b3-3*b2^2/8)^3/216)/sqrt((((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 * b2^2 / 8)^2 / 36)^3)) / 3) + (b3 - 3 *b2^2/8)/6)+(b3-3*b2^2/8))+2*(b4+b2^3/8-b2*b3/2)/sqrt(2*(2*sqrt((((b5 - b2*b4/4 + b2^2*b3/16 - 3*b2^4/256)/3) + (b3 - 3*b2^2/8)^2/36)) * cos(acos(((b3 - 3*b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/12+((b4+b2^3/8-b2*b3/2)^2-4*(b3-3*b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256))/16+(b3-3*b2^2/8)^3/216)/sqrt((((b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/3)+(b3-3*b2^2/8)^2/36)^3))/3)+(b3-3*b2^2/8)/6)-(b3-3*b2^2/8))))/2;
print(x3);

x4 = -1 * b2 / 4 - (sqrt(2 * (2 * sqrt((((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 * b2^2 / 8)^2 / 36) * cos(acos(((b3 - 3 * b2^2 / 8)*(b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 12 + ((b4 + b2^3 / 8 - b2 * b3 / 2)^2 - 4 *(b3 - 3*b2^2/8)*(b5 - b2*b4/4 + b2^2*b3/16 - 3*b2^4/256))/16 + (b3 - 3*b2^2/8)^3/216)/sqrt((((b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/3)+(b3-3*b2^2/8)^2/36)^3))/3)+(b3-3*b2^2/8)/6)-(b3-3*b2^2/8))-sqrt(-(2*(2*sqrt((((b5 - b2 * b4 / 4 + b2^2 * b3 / 16 - 3 * b2^4 / 256) / 3) + (b3 - 3 * b2^2 / 8)^2 / 36)) * cos(acos(((b3 - 3 *b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256)/12+((b4+b2^3/8-b2*b3/2)^2-4*(b3-3*b2^2/8)*(b5-b2*b4/4+b2^2*b3/16-3*b2^4/256))/16+(b3-3*b2^2/8)^3/216)/sqrt((((b5-b2*b4/4 + b2^2 * b3/16 - 3 * b2^4/256)/3) + (b3 - 3 * b2^2/8)^2/36)^3))/3) + (b3 - 3 * b2^2/8)/6) +(b3 - 3*b2^2/8)) + 2*(b4 + b2^3/8 - b2*b3/2)/sqrt(2*(2*sqrt((((b5 - b2*b4/4 + b2^2*b3/16 - 3*b2
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Notes on Solving Quartic Equations in Excel
http://math7755.s1010.xrea.com/Quartic_Equation/Quartic_equation1.htm

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