5b-b(b-6)=8

Solution for 5b-b(b-6)=8 equation:

5b-b(b-6)=8

We move all terms to the left:

5b-b(b-6)-(8)=0

We multiply parentheses

-b^2+5b+6b-8=0

We add all the numbers together, and all the variables

-1b^2+11b-8=0

a = -1; b = 11; c = -8;
Δ = b2-4ac
Δ = 112-4·(-1)·(-8)
Δ = 89
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{-(11)-\sqrt{89}}{2*-1}=\frac{-11-\sqrt{89}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{89}}{2*-1}=\frac{-11+\sqrt{89}}{-2}
$