b(b-15)=30-2b

Solution for b(b-15)=30-2b equation:

b(b-15)=30-2b

We move all terms to the left:

b(b-15)-(30-2b)=0

We add all the numbers together, and all the variables

b(b-15)-(-2b+30)=0

We multiply parentheses

b^2-15b-(-2b+30)=0

We get rid of parentheses

b^2-15b+2b-30=0

We add all the numbers together, and all the variables

b^2-13b-30=0

a = 1; b = -13; c = -30;
Δ = b2-4ac
Δ = -132-4·1·(-30)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*1}=\frac{-4}{2}
=-2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*1}=\frac{30}{2}
=15
$