Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

20 * (y^{2} - 19) / 2 = y^{2} + 54 y + 629 9 y^{2} - 54 y - 819 = 0 9 = 3^{2} 54 = 2 \cdot 3^{3} 819 = 3^{2} \cdot 7 \cdot 13 GCD (9, 54, 819) = 3^{2} = 9 y^{2} - 6 y - 91 = 0 a = 1; b = - 6; c = - 91 D = b^{2} - 4 a c = 6^{2} - 4 \cdot 1 \cdot (- 91) = 400 D > 0 y_{1, 2} = \frac{- b \pm D}{2 a} = \frac{6 \pm 4 0 0}{2} y_{1, 2} = \frac{6 \pm 2 0}{2} y_{1, 2} = 3 \pm 10 y_{1} = 13 y_{2} = - 7 Factored form of the equation: (y - 13) (y + 7) = 0

Solution in text:

9y²-54y-819=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 32400
D > 0 ... The equation has two distinct real roots

y₁ = 13
y₂ = -7

P = {13; -7}