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 * n (n - 1) = (n + 3) * (n + 2) 4 n^{2} - 10 n - 6 = 0 4 = 2^{2} 10 = 2 \cdot 5 6 = 2 \cdot 3 GCD (4, 10, 6) = 2 = 2 2 n^{2} - 5 n - 3 = 0 a = 2; b = - 5; c = - 3 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 2 \cdot (- 3) = 49 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{5 \pm 4 9}{4} n_{1, 2} = \frac{5 \pm 7}{4} n_{1, 2} = 1.25 \pm 1.75 n_{1} = 3 n_{2} = - 0.5 Factored form of the equation: 2 (n - 3) (n + 0.5) = 0

Solution in text:

4n²-10n-6=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 196
D > 0 ... The equation has two distinct real roots

n₁ = 3
n₂ = -0.5

P = {3; -0.5}