X^2-5-8x=5x-4

Solution for X^2-5-8x=5x-4 equation:

X^2-5-8X=5X-4

We move all terms to the left:

X^2-5-8X-(5X-4)=0

We get rid of parentheses

X^2-8X-5X+4-5=0

We add all the numbers together, and all the variables

X^2-13X-1=0

a = 1; b = -13; c = -1;
Δ = b2-4ac
Δ = -132-4·1·(-1)
Δ = 173
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{173}}{2*1}=\frac{13-\sqrt{173}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{173}}{2*1}=\frac{13+\sqrt{173}}{2}
$