6x^2+24x+18=378

Solution for 6x^2+24x+18=378 equation:

6x^2+24x+18=378

We move all terms to the left:

6x^2+24x+18-(378)=0

We add all the numbers together, and all the variables

6x^2+24x-360=0

a = 6; b = 24; c = -360;
Δ = b2-4ac
Δ = 242-4·6·(-360)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-96}{2*6}=\frac{-120}{12}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+96}{2*6}=\frac{72}{12}
=6
$