3x^2+86x-578=0

Solution for 3x^2+86x-578=0 equation:

3x^2+86x-578=0

a = 3; b = 86; c = -578;
Δ = b2-4ac
Δ = 862-4·3·(-578)
Δ = 14332
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14332}=\sqrt{4*3583}=\sqrt{4}*\sqrt{3583}=2\sqrt{3583}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-2\sqrt{3583}}{2*3}=\frac{-86-2\sqrt{3583}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+2\sqrt{3583}}{2*3}=\frac{-86+2\sqrt{3583}}{6}
$