g^2+6=13g-16

Solution for g^2+6=13g-16 equation:

g^2+6=13g-16

We move all terms to the left:

g^2+6-(13g-16)=0

We get rid of parentheses

g^2-13g+16+6=0

We add all the numbers together, and all the variables

g^2-13g+22=0

a = 1; b = -13; c = +22;
Δ = b2-4ac
Δ = -132-4·1·22
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-9}{2*1}=\frac{4}{2}
=2
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+9}{2*1}=\frac{22}{2}
=11
$