2x(3x+6)=378

Solution for 2x(3x+6)=378 equation:

2x(3x+6)=378

We move all terms to the left:

2x(3x+6)-(378)=0

We multiply 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{-108}{12}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+96}{2*6}=\frac{84}{12}
=7
$