X^2-2x-8=100

Solution for X^2-2x-8=100 equation:

X^2-2X-8=100

We move all terms to the left:

X^2-2X-8-(100)=0

We add all the numbers together, and all the variables

X^2-2X-108=0

a = 1; b = -2; c = -108;
Δ = b2-4ac
Δ = -22-4·1·(-108)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{109}}{2*1}=\frac{2-2\sqrt{109}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{109}}{2*1}=\frac{2+2\sqrt{109}}{2}
$