b(b+30)=32175

Solution for b(b+30)=32175 equation:

b(b+30)=32175

We move all terms to the left:

b(b+30)-(32175)=0

We multiply parentheses

b^2+30b-32175=0

a = 1; b = 30; c = -32175;
Δ = b2-4ac
Δ = 302-4·1·(-32175)
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-360}{2*1}=\frac{-390}{2}
=-195
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+360}{2*1}=\frac{330}{2}
=165
$