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 * x * (x - 1) - 3 * (x + 1) * x / 2 - x * 2 = 0 2.5 x^{2} - 7.5 x = 0 a = 2.5; b = - 7.5; c = 0 D = b^{2} - 4 a c = 7 . 5^{2} - 4 \cdot 2.5 \cdot 0 = 56.25 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{7 . 5 \pm 5 6 . 2 5}{5} x_{1, 2} = 1.5 \pm 1.5 x_{1} = 3 x_{2} = 0 Factored form of the equation: 2.5 (x - 3) x = 0

Solution in text:

2.5x²-7.5x=0 ... c=0; quadratic equation without constant term

Discriminant:
D = b² - 4ac = 56.25
D > 0 ... The equation has two distinct real roots

x₁ = 3
x₂ = 0

P = {3; 0}