100=12x+2x^2

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

100=12x+2x^2

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = -12; c = +100;
Δ = b2-4ac
Δ = -122-4·(-2)·100
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{59}}{2*-2}=\frac{12-4\sqrt{59}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{59}}{2*-2}=\frac{12+4\sqrt{59}}{-4}
$