Quadratic equation calculator

Quadratic equation has the basic form:

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

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

13 0^{2} = a^{2} + (170 - a)^{2} - 2 a^{2} + 340 a - 12000 = 0 2 a^{2} - 340 a + 12000 = 0 2 . . . prime number 340 = 2^{2} \cdot 5 \cdot 17 12000 = 2^{5} \cdot 3 \cdot 5^{3} GCD (2, 340, 12000) = 2 = 2 a^{2} - 170 a + 6000 = 0 p = 1; q = - 170; r = 6000 D = q^{2} - 4 p r = 17 0^{2} - 4 \cdot 1 \cdot 6000 = 4900 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 7 0 \pm 4 9 0 0}{2} a_{1, 2} = \frac{1 7 0 \pm 7 0}{2} a_{1, 2} = 85 \pm 35 a_{1} = 120 a_{2} = 50 Factored form of the equation: (a - 120) (a - 50) = 0

Solution in text:

-2a²+340a-12000=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 19600
D > 0 ... The equation has two distinct real roots

a₁ = 120
a₂ = 50

P = {120; 50}