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:

3 x^{2} - 3 x - (- 6 x^{2} - x + 7) = - 2 9 x^{2} - 2 x - 5 = 0 a = 9; b = - 2; c = - 5 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 9 \cdot (- 5) = 184 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 \pm 1 8 4}{1 8} = \frac{2 \pm 2 4 6}{1 8} x_{1, 2} = 0.111111 \pm 0.753592 x_{1} = 0.864703331 x_{2} = - 0.642481109 Factored form of the equation: 9 (x - 0.864703331) (x + 0.642481109) = 0

Solution in text:

9x²-2x-5=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 184
D > 0 ... The equation has two distinct real roots

x₁ = 0.8647033
x₂ = -0.6424811

P = {0.8647033; -0.6424811}