b+2b(b+16)=180

Solution for b+2b(b+16)=180 equation:

b+2b(b+16)=180

We move all terms to the left:

b+2b(b+16)-(180)=0

We multiply parentheses

2b^2+b+32b-180=0

We add all the numbers together, and all the variables

2b^2+33b-180=0

a = 2; b = 33; c = -180;
Δ = b2-4ac
Δ = 332-4·2·(-180)
Δ = 2529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2529}=\sqrt{9*281}=\sqrt{9}*\sqrt{281}=3\sqrt{281}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{281}}{2*2}=\frac{-33-3\sqrt{281}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{281}}{2*2}=\frac{-33+3\sqrt{281}}{4}
$