2x^2+12x=x^2+8

Solution for 2x^2+12x=x^2+8 equation:

2x^2+12x=x^2+8

We move all terms to the left:

2x^2+12x-(x^2+8)=0

We get rid of parentheses

2x^2-x^2+12x-8=0

We add all the numbers together, and all the variables

x^2+12x-8=0

a = 1; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·1·(-8)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{11}}{2*1}=\frac{-12-4\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{11}}{2*1}=\frac{-12+4\sqrt{11}}{2}
$