8x^2-11=8x

Solution for 8x^2-11=8x equation:

8x^2-11=8x

We move all terms to the left:

8x^2-11-(8x)=0

a = 8; b = -8; c = -11;
Δ = b2-4ac
Δ = -82-4·8·(-11)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{26}}{2*8}=\frac{8-4\sqrt{26}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{26}}{2*8}=\frac{8+4\sqrt{26}}{16}
$