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:

t^{2} + 11 t - 12 = 0 t^{2} + 11 t - 12 = 0 a = 1; b = 11; c = - 12 D = b^{2} - 4 a c = 1 1^{2} - 4 \cdot 1 \cdot (- 12) = 169 D > 0 t_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 1 \pm 1 6 9}{2} t_{1, 2} = \frac{- 1 1 \pm 1 3}{2} t_{1, 2} = - 5.5 \pm 6.5 t_{1} = 1 t_{2} = - 12 Factored form of the equation: (t - 1) (t + 12) = 0

Solution in text:

t²+11t-12=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 169
D > 0 ... The equation has two distinct real roots

t₁ = 1
t₂ = -12

P = {1; -12}