6x^2-18x-24=216

Solution for 6x^2-18x-24=216 equation:

6x^2-18x-24=216

We move all terms to the left:

6x^2-18x-24-(216)=0

We add all the numbers together, and all the variables

6x^2-18x-240=0

a = 6; b = -18; c = -240;
Δ = b2-4ac
Δ = -182-4·6·(-240)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-78}{2*6}=\frac{-60}{12}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+78}{2*6}=\frac{96}{12}
=8
$