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 0^{2} = (x + 34)^{2} + x^{2} - 2 x^{2} - 68 x + 1344 = 0 2 x^{2} + 68 x - 1344 = 0 2 . . . prime number 68 = 2^{2} \cdot 17 1344 = 2^{6} \cdot 3 \cdot 7 GCD (2, 68, 1344) = 2 = 2 x^{2} + 34 x - 672 = 0 a = 1; b = 34; c = - 672 D = b^{2} - 4 a c = 3 4^{2} - 4 \cdot 1 \cdot (- 672) = 3844 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 3 4 \pm 3 8 4 4}{2} x_{1, 2} = \frac{- 3 4 \pm 6 2}{2} x_{1, 2} = - 17 \pm 31 x_{1} = 14 x_{2} = - 48 Factored form of the equation: (x - 14) (x + 48) = 0

Solution in text:

-2x²-68x+1344=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 15376
D > 0 ... The equation has two distinct real roots

x₁ = 14
x₂ = -48

P = {14; -48}