X2-8x-20=90

Solution for X2-8x-20=90 equation:

X2-8X-20=90

We move all terms to the left:

X2-8X-20-(90)=0

We add all the numbers together, and all the variables

X^2-8X-110=0

a = 1; b = -8; c = -110;
Δ = b2-4ac
Δ = -82-4·1·(-110)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{14}}{2*1}=\frac{8-6\sqrt{14}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{14}}{2*1}=\frac{8+6\sqrt{14}}{2}
$