-6x^2-54x-24=0

Solution for -6x^2-54x-24=0 equation:

-6x^2-54x-24=0

a = -6; b = -54; c = -24;
Δ = b2-4ac
Δ = -542-4·(-6)·(-24)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{65}}{2*-6}=\frac{54-6\sqrt{65}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{65}}{2*-6}=\frac{54+6\sqrt{65}}{-12}
$