100=8x^2+12x

Solution for 100=8x^2+12x equation:

100=8x^2+12x

We move all terms to the left:

100-(8x^2+12x)=0

We get rid of parentheses

-8x^2-12x+100=0

a = -8; b = -12; c = +100;
Δ = b2-4ac
Δ = -122-4·(-8)·100
Δ = 3344
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:

$\sqrt{\Delta}=\sqrt{3344}=\sqrt{16*209}=\sqrt{16}*\sqrt{209}=4\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{209}}{2*-8}=\frac{12-4\sqrt{209}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{209}}{2*-8}=\frac{12+4\sqrt{209}}{-16}
$