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:

6 x * (3 x - 2) + 7 x = 0 18 x^{2} - 5 x = 0 a = 18; b = - 5; c = 0 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 18 \cdot 0 = 25 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{5 \pm 2 5}{3 6} x_{1, 2} = \frac{5 \pm 5}{3 6} x_{1, 2} = 0.138889 \pm 0.138889 x_{1} = 0.277777778 x_{2} = 0 Factored form of the equation: 18 (x - 0.277777778) x = 0

Solution in text:

18x²-5x=0 ... c=0; quadratic equation without constant term

Discriminant:
D = b² - 4ac = 25
D > 0 ... The equation has two distinct real roots

x₁ = 0.2777778
x₂ = 0

P = {0.2777778; 0}