X^2-19=8x

Solution for X^2-19=8x equation:

X^2-19=8X

We move all terms to the left:

X^2-19-(8X)=0

a = 1; b = -8; c = -19;
Δ = b2-4ac
Δ = -82-4·1·(-19)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{35}}{2*1}=\frac{8-2\sqrt{35}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{35}}{2*1}=\frac{8+2\sqrt{35}}{2}
$