-5^3-5b=5b^2-180

Solution for -5^3-5b=5b^2-180 equation:

-5^3-5b=5b^2-180

We move all terms to the left:

-5^3-5b-(5b^2-180)=0

We add all the numbers together, and all the variables

-5b-(5b^2-180)-125=0

We get rid of parentheses

-5b^2-5b+180-125=0

We add all the numbers together, and all the variables

-5b^2-5b+55=0

a = -5; b = -5; c = +55;
Δ = b2-4ac
Δ = -52-4·(-5)·55
Δ = 1125
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:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15\sqrt{5}}{2*-5}=\frac{5-15\sqrt{5}}{-10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15\sqrt{5}}{2*-5}=\frac{5+15\sqrt{5}}{-10}
$