Quadratic Equation Calculator

A quadratic equation has the basic form:

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

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

10 * P + P + P * P + P = 160 P^{2} + 12 P - 160 = 0 a = 1; b = 12; c = - 160 D = b^{2} - 4 a c = 1 2^{2} - 4 \cdot 1 \cdot (- 160) = 784 D > 0 P_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 2 \pm 7 8 4}{2} P_{1, 2} = \frac{- 1 2 \pm 2 8}{2} P_{1, 2} = - 6 \pm 14 P_{1} = 8 P_{2} = - 20 Factored form of the equation: (P - 8) (P + 20) = 0

Solution in text:

P²+12P-160=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 784
D > 0 ... The equation has two distinct real roots

P₁ = 8
P₂ = -20

P = {8; -20}