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:

4 t + 5 (t - 5) = t (t - 5) - t^{2} + 14 t - 25 = 0 t^{2} - 14 t + 25 = 0 a = 1; b = - 14; c = 25 D = b^{2} - 4 a c = 1 4^{2} - 4 \cdot 1 \cdot 25 = 96 D > 0 t_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 4 \pm 9 6}{2} = \frac{1 4 \pm 4 6}{2} t_{1, 2} = 7 \pm 4.898979 t_{1} = 11.898979486 t_{2} = 2.101020514 Factored form of the equation: (t - 11.898979486) (t - 2.101020514) = 0

Solution in text:

-t²+14t-25=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 96
D > 0 ... The equation has two distinct real roots

t₁ = 11.8989795
t₂ = 2.1010205

P = {11.8989795; 2.1010205}