-3x^2-54x+51=0

Solution for -3x^2-54x+51=0 equation:

-3x^2-54x+51=0

a = -3; b = -54; c = +51;
Δ = b2-4ac
Δ = -542-4·(-3)·51
Δ = 3528
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:

$\sqrt{\Delta}=\sqrt{3528}=\sqrt{1764*2}=\sqrt{1764}*\sqrt{2}=42\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-42\sqrt{2}}{2*-3}=\frac{54-42\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+42\sqrt{2}}{2*-3}=\frac{54+42\sqrt{2}}{-6}
$