5b^2-116=-9b

Solution for 5b^2-116=-9b equation:

5b^2-116=-9b

We move all terms to the left:

5b^2-116-(-9b)=0

We get rid of parentheses

5b^2+9b-116=0

a = 5; b = 9; c = -116;
Δ = b2-4ac
Δ = 92-4·5·(-116)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-49}{2*5}=\frac{-58}{10}
=-5+4/5
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+49}{2*5}=\frac{40}{10}
=4
$