31b^2+87b-18=3b+b^2

Solution for 31b^2+87b-18=3b+b^2 equation:

31b^2+87b-18=3b+b^2

We move all terms to the left:

31b^2+87b-18-(3b+b^2)=0

We get rid of parentheses

31b^2-b^2-3b+87b-18=0

We add all the numbers together, and all the variables

30b^2+84b-18=0

a = 30; b = 84; c = -18;
Δ = b2-4ac
Δ = 842-4·30·(-18)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-96}{2*30}=\frac{-180}{60}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+96}{2*30}=\frac{12}{60}
=1/5
$