-3x^2-18x+512=0

Solution for -3x^2-18x+512=0 equation:

-3x^2-18x+512=0

a = -3; b = -18; c = +512;
Δ = b2-4ac
Δ = -182-4·(-3)·512
Δ = 6468
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:

$\sqrt{\Delta}=\sqrt{6468}=\sqrt{196*33}=\sqrt{196}*\sqrt{33}=14\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-14\sqrt{33}}{2*-3}=\frac{18-14\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+14\sqrt{33}}{2*-3}=\frac{18+14\sqrt{33}}{-6}
$