4b(b+95)=180

Solution for 4b(b+95)=180 equation:

4b(b+95)=180

We move all terms to the left:

4b(b+95)-(180)=0

We multiply parentheses

4b^2+380b-180=0

a = 4; b = 380; c = -180;
Δ = b2-4ac
Δ = 3802-4·4·(-180)
Δ = 147280
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:

$\sqrt{\Delta}=\sqrt{147280}=\sqrt{16*9205}=\sqrt{16}*\sqrt{9205}=4\sqrt{9205}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(380)-4\sqrt{9205}}{2*4}=\frac{-380-4\sqrt{9205}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(380)+4\sqrt{9205}}{2*4}=\frac{-380+4\sqrt{9205}}{8}
$