g^2+11g+30.25=90.25

Solution for g^2+11g+30.25=90.25 equation:

g^2+11g+30.25=90.25

We move all terms to the left:

g^2+11g+30.25-(90.25)=0

We add all the numbers together, and all the variables

g^2+11g-60=0

a = 1; b = 11; c = -60;
Δ = b2-4ac
Δ = 112-4·1·(-60)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*1}=\frac{-30}{2}
=-15
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*1}=\frac{8}{2}
=4
$