(x^2)-5x=8

Solution for (x^2)-5x=8 equation:

(x^2)-5x=8

We move all terms to the left:

(x^2)-5x-(8)=0

a = 1; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·1·(-8)
Δ = 57
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{-(-5)-\sqrt{57}}{2*1}=\frac{5-\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*1}=\frac{5+\sqrt{57}}{2}
$