g(2g-1)=13g

Solution for g(2g-1)=13g equation:

g(2g-1)=13g

We move all terms to the left:

g(2g-1)-(13g)=0

We add all the numbers together, and all the variables

-13g+g(2g-1)=0

We multiply parentheses

2g^2-13g-1g=0

We add all the numbers together, and all the variables

2g^2-14g=0

a = 2; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·2·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*2}=\frac{0}{4}
=0
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*2}=\frac{28}{4}
=7
$