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:

1570 = 2 * p i * r (r + 15) - 6.2831853071798 r^{2} - 94.248 r + 1570 = 0 6.2831853071798 r^{2} + 94.248 r - 1570 = 0 a = 6.283185; b = 94.248; c = - 1570 D = b^{2} - 4 a c = 94.24 8^{2} - 4 \cdot 6.283185 \cdot (- 1570) = 48341.047690069 D > 0 r_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 9 4 . 2 5 \pm 4 8 3 4 1 . 0 5}{1 2 . 5 6 6 3 7 1} r_{1, 2} = - 7.5 \pm 17.496379 r_{1} = 9.996378501 r_{2} = - 24.996378501 Factored form of the equation: 6.2831853071798 (r - 9.996378501) (r + 24.996378501) = 0

Solution in text:

-6.2831853071798r²-94.247779607694r+1570=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 48341.047690069
D > 0 ... The equation has two distinct real roots

r₁ = 9.9963785
r₂ = -24.9963785

P = {9.9963785; -24.9963785}