b(b-5)=8

Solution for b(b-5)=8 equation:

b(b-5)=8

We move all terms to the left:

b(b-5)-(8)=0

We multiply parentheses

b^2-5b-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:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{57}}{2*1}=\frac{5-\sqrt{57}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*1}=\frac{5+\sqrt{57}}{2}
$