100=x^2-12x-18

Solution for 100=x^2-12x-18 equation:

100=x^2-12x-18

We move all terms to the left:

100-(x^2-12x-18)=0

We get rid of parentheses

-x^2+12x+18+100=0

We add all the numbers together, and all the variables

-1x^2+12x+118=0

a = -1; b = 12; c = +118;
Δ = b2-4ac
Δ = 122-4·(-1)·118
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{154}}{2*-1}=\frac{-12-2\sqrt{154}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{154}}{2*-1}=\frac{-12+2\sqrt{154}}{-2}
$