Quadratic equation calculator

Quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

5 0^{2} = 6 0^{2} + c^{2} - 2 * 60 * c * 0.17364817766693 - c^{2} + 20.838 c - 1100 = 0 c^{2} - 20.838 c + 1100 = 0 p = 1; q = - 20.838; r = 1100 D = q^{2} - 4 p r = 20.83 8^{2} - 4 \cdot 1 \cdot 1100 = - 3965.7868696585 D < 0 c_{1, 2} = \frac{- q \pm D}{2 p} = \frac{2 0 . 8 4 \pm - 3 9 6 5 . 7 9}{2} c_{1, 2} = \frac{2 0 . 8 4 \pm i 3 9 6 5 . 7 9}{2} c_{1, 2} = 10.418891 \pm 31.487247 i c_{1} = 10.418891 + 31.48724690116 i c_{2} = 10.418891 - 31.48724690116 i Factored form of the equation: (c - 10.418891 - 31.48724690116 i) (c - 10.418891 + 31.48724690116 i) = 0

Solution in text:

-c²+20.837781320032c-1100=0 ... quadratic equation

Discriminant:
D = b² - 4ac = -3965.7868696585
D < 0 ... The equation has two distinct complex roots

c₁ = 10.4188907+31.4872469i
c₂ = 10.4188907-31.4872469i

P = {10.4188907+31.4872469i; 10.4188907-31.4872469i}