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:

5 x + x^{2} - 100 = 0 x^{2} + 5 x - 100 = 0 a = 1; b = 5; c = - 100 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 1 \cdot (- 100) = 425 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 5 \pm 4 2 5}{2} = \frac{- 5 \pm 5 1 7}{2} x_{1, 2} = - 2.5 \pm 10.307764 x_{1} = 7.807764064 x_{2} = - 12.807764064 Factored form of the equation: (x - 7.807764064) (x + 12.807764064) = 0

Solution in text:

x²+5x-100=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 425
D > 0 ... The equation has two distinct real roots

x₁ = 7.8077641
x₂ = -12.8077641

P = {7.8077641; -12.8077641}