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:

3 * 1813 / 7 = a^{2} + a * (a - 6) + (a - 6)^{2} - 3 a^{2} + 18 a + 741 = 0 3 a^{2} - 18 a - 741 = 0 3 . . . prime number 18 = 2 \cdot 3^{2} 741 = 3 \cdot 13 \cdot 19 GCD (3, 18, 741) = 3 = 3 a^{2} - 6 a - 247 = 0 p = 1; q = - 6; r = - 247 D = q^{2} - 4 p r = 6^{2} - 4 \cdot 1 \cdot (- 247) = 1024 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{6 \pm 1 0 2 4}{2} a_{1, 2} = \frac{6 \pm 3 2}{2} a_{1, 2} = 3 \pm 16 a_{1} = 19 a_{2} = - 13 Factored form of the equation: (a - 19) (a + 13) = 0

Solution in text:

-3a²+18a+741=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 9216
D > 0 ... The equation has two distinct real roots

a₁ = 19
a₂ = -13

P = {19; -13}