Quadratic Equation (2nd Degree Polynomial) Solution:a*(x^2) + b*(x) + c = 0

Input Equation Coefficients:a = 2.0000

b = 8.0000

c = -10.0000

Roots of Quadratic Equation:x1 = 1.0000 = (-b+SQRT(b^2-4*a*c))/(2*a)

x2 = -5.0000 = (-b-SQRT(b^2-4*a*c))/(2*a)

Cubic Equation (3rd Degree Polynomial) Solution:a*(x^3) + b*(x^2) + c*(x) + d = 0

Input Equation Coefficients:a = 2.0000

b = -4.0000

c = -22.0000

d = 24.0000

Solve Cubic Equation:f = -12.333 = ((3*c/a)-(b^2/a^2))/3

g = 4.074 = ((2*b^3/a^3)-(9*b*c/a^2)+(27*d/a))/27h = -65.333 = (g^2/4)+(f^3/27)i = 8.336 = SQRT((g^2/4)-h)j = 2.028 = i^(1/3)

k = 1.818 = ACOS(-(g/(2*i)))L = -2.028 = j*(-1)M = 0.822 = COS(k/3)N = 0.986 = SQRT(3)*SIN(k/3)P = 0.667 = (b/(3*a))*(-1)R = N.A. = -(g/2)+SQRT(h)S = N.A. = R^(1/3)T = N.A. = -(g/2)-SQRT(h)U = N.A. = T^(1/3)

Roots of Cubic Equation:Case #1: If h > 0 Case #2: If h <= 0 Case #3: If f, g, h = 0

x1 = N.A. 4.0000 N.A. = 2*j*COS(k/3)-(b/(3*a))x2 = N.A. -3.0000 N.A. = L*(M+N)+Px3 = N.A. 1.0000 N.A. = L*(M-N)+P

Quartic Equation (4th Degree Polynomial) Solution:a*(x^4) + b*(x^3) + c*(x^2) + d*(x) + e = 0

Input Equation Coefficients: Modified Coefficients (dividing each by 'a'):

a = 3.0000 ao = 1.0000 = a/ab = 6.0000 bo = 2.0000 = b/ac = -123.0000 co = -41.0000 = c/ad = -126.0000 do = -42.0000 = d/a

e = 1080.0000 eo = 360.0000 = e/a

f = -42.500 = co-(3*bo^2/8)g = 0.000 = do+(bo^3/8)-(bo*co/2)h = 370.563 = eo-(3*bo^4/256)+(bo^2*co/16)-(bo*do/4)

Substitute 'f', 'g', and 'h' into following Cubic Equation:(y^3) + (f/2)*(y^2) + ((f^2-4*h)/16*y - g^2/64 = 0

a1 = 1.000 = 1b1 = -21.250 = (f/2)c1 = 20.250 = ((f^2-4*h)/16d1 = 0.000 = -(g^2/64)

Solve Cubic Equation:f1 = -130.271 = ((3*c1/a1)-(b1^2/a1^2))/3g1 = -567.355 = ((2*b1^3/a1^3)-(9*b1*c1/a1^2)+(27*d1/a1))/27h1 = -1406.979 = (g1^2/4)+(f1^3/27)

i = 286.147 = SQRT((g1^2/4)-h1)j = 6.590 = i^(1/3)

k = 0.131 = ACOS(-(g1/(2*i)))L = -6.590 = j*(-1)M = 0.999 = COS(k/3)N = 0.076 = SQRT(3)*SIN(k/3)P = 7.083 = (b1/(3*a1))*(-1)

R = N.A. = -(g1/2)+SQRT(h1)

S = N.A. = R^(1/3)

T = N.A. = -(g1/2)-SQRT(h1)

U = N.A. = T^(1/3)Roots of Cubic Equation:Case #1: If h1 > 0 Case #2: If h1 <= 0 Case #3: If f1, g1, h1 = 0

y1 = N.A. 20.2500 N.A. = 2*j*COS(k/3)-(b/(3*a1))y2 = N.A. 0.0000 N.A. = L*(M+N)+Py3 = N.A. 1.0000 N.A. = L*(M-N)+P

p = 4.5000 = SQRT(y1)q = 1.0000 = SQRT(y3)r = 0.0000 = -g/(8*p*q)s = 0.5000 = b/(4*a)

Roots of Quartic Equation:x1 = 5.0000 = p+q+r-sx2 = 3.0000 = p-q-r-sx3 = -4.0000 = -p+q-r-s

x4 = -6.0000 = -p-q+r-s