4b(b+48)=180

Solution for 4b(b+48)=180 equation:

4b(b+48)=180

We move all terms to the left:

4b(b+48)-(180)=0

We multiply parentheses

4b^2+192b-180=0

a = 4; b = 192; c = -180;
Δ = b2-4ac
Δ = 1922-4·4·(-180)
Δ = 39744
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:

$\sqrt{\Delta}=\sqrt{39744}=\sqrt{576*69}=\sqrt{576}*\sqrt{69}=24\sqrt{69}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-24\sqrt{69}}{2*4}=\frac{-192-24\sqrt{69}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+24\sqrt{69}}{2*4}=\frac{-192+24\sqrt{69}}{8}
$