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 * (100 - a) * (100 - a) * 15 = a^{2} * (6 * 3 + 2) 25 a^{2} - 9000 a + 450000 = 0 25 = 5^{2} 9000 = 2^{3} \cdot 3^{2} \cdot 5^{3} 450000 = 2^{4} \cdot 3^{2} \cdot 5^{5} GCD (25, 9000, 450000) = 5^{2} = 25 a^{2} - 360 a + 18000 = 0 p = 1; q = - 360; r = 18000 D = q^{2} - 4 p r = 36 0^{2} - 4 \cdot 1 \cdot 18000 = 57600 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{3 6 0 \pm 5 7 6 0 0}{2} a_{1, 2} = \frac{3 6 0 \pm 2 4 0}{2} a_{1, 2} = 180 \pm 120 a_{1} = 300 a_{2} = 60 Factored form of the equation: (a - 300) (a - 60) = 0

Solution in text:

25a²-9000a+450000=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 36000000
D > 0 ... The equation has two distinct real roots

a₁ = 300
a₂ = 60

P = {300; 60}