b^2+5b-35+3b=180

Solution for b^2+5b-35+3b=180 equation:

b^2+5b-35+3b=180

We move all terms to the left:

b^2+5b-35+3b-(180)=0

We add all the numbers together, and all the variables

b^2+8b-215=0

a = 1; b = 8; c = -215;
Δ = b2-4ac
Δ = 82-4·1·(-215)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{231}}{2*1}=\frac{-8-2\sqrt{231}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{231}}{2*1}=\frac{-8+2\sqrt{231}}{2}
$