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:

4 t + 0.5 * 0.5 * t^{2} = 10 * t + 0.5 * (- 1) * t^{2} 0.75 t^{2} - 6 t = 0 a = 0.75; b = - 6; c = 0 D = b^{2} - 4 a c = 6^{2} - 4 \cdot 0.75 \cdot 0 = 36 D > 0 t_{1, 2} = \frac{- b \pm D}{2 a} = \frac{6 \pm 3 6}{1 . 5} t_{1, 2} = \frac{6 \pm 6}{1 . 5} t_{1, 2} = 4 \pm 4 t_{1} = 8 t_{2} = 0 Factored form of the equation: 0.75 (t - 8) t = 0

Solution in text:

0.75t²-6t=0 ... c=0; quadratic equation without constant term

Discriminant:
D = b² - 4ac = 36
D > 0 ... The equation has two distinct real roots

t₁ = 8
t₂ = 0

P = {8; 0}