1008=2x^2+12x

Solution for 1008=2x^2+12x equation:

1008=2x^2+12x

We move all terms to the left:

1008-(2x^2+12x)=0

We get rid of parentheses

-2x^2-12x+1008=0

a = -2; b = -12; c = +1008;
Δ = b2-4ac
Δ = -122-4·(-2)·1008
Δ = 8208
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:

$\sqrt{\Delta}=\sqrt{8208}=\sqrt{144*57}=\sqrt{144}*\sqrt{57}=12\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{57}}{2*-2}=\frac{12-12\sqrt{57}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{57}}{2*-2}=\frac{12+12\sqrt{57}}{-4}
$