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:

240 = (4 + 6) * t + 0.5 * (3 + 2) * t^{2} - 2.5 t^{2} - 10 t + 240 = 0 2.5 t^{2} + 10 t - 240 = 0 a = 2.5; b = 10; c = - 240 D = b^{2} - 4 a c = 1 0^{2} - 4 \cdot 2.5 \cdot (- 240) = 2500 D > 0 t_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 0 \pm 2 5 0 0}{5} t_{1, 2} = \frac{- 1 0 \pm 5 0}{5} t_{1, 2} = - 2 \pm 10 t_{1} = 8 t_{2} = - 12 Factored form of the equation: 2.5 (t - 8) (t + 12) = 0

Solution in text:

-2.5t²-10t+240=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 2500
D > 0 ... The equation has two distinct real roots

t₁ = 8
t₂ = -12

P = {8; -12}