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:

400 * m * 100 = 400 * 100 * (m + 300) - 5 * (m + 300) * m 5 m^{2} + 1500 m - 12000000 = 0 5 . . . prime number 1500 = 2^{2} \cdot 3 \cdot 5^{3} 12000000 = 2^{8} \cdot 3 \cdot 5^{6} GCD (5, 1500, 12000000) = 5 = 5 m^{2} + 300 m - 2400000 = 0 a = 1; b = 300; c = - 2400000 D = b^{2} - 4 a c = 30 0^{2} - 4 \cdot 1 \cdot (- 2400000) = 9690000 D > 0 m_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 3 0 0 \pm 9 6 9 0 0 0 0}{2} = \frac{- 3 0 0 \pm 1 0 0 9 6 9}{2} m_{1, 2} = - 150 \pm 1556.438242 m_{1} = 1406.438241627 m_{2} = - 1706.438241627 Factored form of the equation: (m - 1406.438241627) (m + 1706.438241627) = 0

Solution in text:

5m²+1500m-12000000=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 242250000
D > 0 ... The equation has two distinct real roots

m₁ = 1406.4382416
m₂ = -1706.4382416

P = {1406.4382416; -1706.4382416}