0=6x^2+12x-378

Solution for 0=6x^2+12x-378 equation:

0=6x^2+12x-378

We move all terms to the left:

0-(6x^2+12x-378)=0

We add all the numbers together, and all the variables

-(6x^2+12x-378)=0

We get rid of parentheses

-6x^2-12x+378=0

a = -6; b = -12; c = +378;
Δ = b2-4ac
Δ = -122-4·(-6)·378
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{-(-12)-96}{2*-6}=\frac{-84}{-12}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+96}{2*-6}=\frac{108}{-12}
=-9
$