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:

16 * 6^{2} + 216 * 6 + 16 * y^{2} - 400 * y + 304 = 0 16 y^{2} - 400 y + 2176 = 0 16 = 2^{4} 400 = 2^{4} \cdot 5^{2} 2176 = 2^{7} \cdot 17 GCD (16, 400, 2176) = 2^{4} = 16 y^{2} - 25 y + 136 = 0 a = 1; b = - 25; c = 136 D = b^{2} - 4 a c = 2 5^{2} - 4 \cdot 1 \cdot 136 = 81 D > 0 y_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 5 \pm 8 1}{2} y_{1, 2} = \frac{2 5 \pm 9}{2} y_{1, 2} = 12.5 \pm 4.5 y_{1} = 17 y_{2} = 8 Factored form of the equation: (y - 17) (y - 8) = 0

Solution in text:

16y²-400y+2176=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 20736
D > 0 ... The equation has two distinct real roots

y₁ = 17
y₂ = 8

P = {17; 8}