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:

29 b^{2} + 4 b = 480 29 b^{2} + 4 b - 480 = 0 p = 29; q = 4; r = - 480 D = q^{2} - 4 p r = 4^{2} - 4 \cdot 29 \cdot (- 480) = 55696 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 4 \pm 5 5 6 9 6}{5 8} b_{1, 2} = \frac{- 4 \pm 2 3 6}{5 8} b_{1, 2} = - 0.068966 \pm 4.068966 b_{1} = 4 b_{2} = - 4.137931034 Factored form of the equation: 29 (b - 4) (b + 4.137931034) = 0

Solution in text:

29b²+4b-480=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 55696
D > 0 ... The equation has two distinct real roots

b₁ = 4
b₂ = -4.137931

P = {4; -4.137931}