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:

50 b = 2 b^{2} + 20 b + 2 * 20 - 2 b^{2} + 30 b - 40 = 0 2 b^{2} - 30 b + 40 = 0 2 . . . prime number 30 = 2 \cdot 3 \cdot 5 40 = 2^{3} \cdot 5 GCD (2, 30, 40) = 2 = 2 b^{2} - 15 b + 20 = 0 p = 1; q = - 15; r = 20 D = q^{2} - 4 p r = 1 5^{2} - 4 \cdot 1 \cdot 20 = 145 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 5 \pm 1 4 5}{2} b_{1, 2} = 7.5 \pm 6.020797 b_{1} = 13.520797289 b_{2} = 1.479202711 Factored form of the equation: (b - 13.520797289) (b - 1.479202711) = 0

Solution in text:

-2b²+30b-40=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 580
D > 0 ... The equation has two distinct real roots

b₁ = 13.5207973
b₂ = 1.4792027

P = {13.5207973; 1.4792027}