5b(b+56)=180

Solution for 5b(b+56)=180 equation:

5b(b+56)=180

We move all terms to the left:

5b(b+56)-(180)=0

We multiply parentheses

5b^2+280b-180=0

a = 5; b = 280; c = -180;
Δ = b2-4ac
Δ = 2802-4·5·(-180)
Δ = 82000
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:

$\sqrt{\Delta}=\sqrt{82000}=\sqrt{400*205}=\sqrt{400}*\sqrt{205}=20\sqrt{205}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-20\sqrt{205}}{2*5}=\frac{-280-20\sqrt{205}}{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+20\sqrt{205}}{2*5}=\frac{-280+20\sqrt{205}}{10}
$