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:

250 = 25 * t + 0.5 * 5 * t^{2} - 2.5 t^{2} - 25 t + 250 = 0 2.5 t^{2} + 25 t - 250 = 0 a = 2.5; b = 25; c = - 250 D = b^{2} - 4 a c = 2 5^{2} - 4 \cdot 2.5 \cdot (- 250) = 3125 D > 0 t_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 2 5 \pm 3 1 2 5}{5} = \frac{- 2 5 \pm 2 5 5}{5} t_{1, 2} = - 5 \pm 11.18034 t_{1} = 6.180339887 t_{2} = - 16.180339887 Factored form of the equation: 2.5 (t - 6.180339887) (t + 16.180339887) = 0

Solution in text:

-2.5t²-25t+250=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 3125
D > 0 ... The equation has two distinct real roots

t₁ = 6.1803399
t₂ = -16.1803399

P = {6.1803399; -16.1803399}