X2-11=8x

Solution for X2-11=8x equation:

X2-11=8X

We move all terms to the left:

X2-11-(8X)=0

We add all the numbers together, and all the variables

X^2-8X-11=0

a = 1; b = -8; c = -11;
Δ = b2-4ac
Δ = -82-4·1·(-11)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{3}}{2*1}=\frac{8-6\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{3}}{2*1}=\frac{8+6\sqrt{3}}{2}
$