6g(2g-1)=13g

Solution for 6g(2g-1)=13g equation:

6g(2g-1)=13g

We move all terms to the left:

6g(2g-1)-(13g)=0

We add all the numbers together, and all the variables

-13g+6g(2g-1)=0

We multiply parentheses

12g^2-13g-6g=0

We add all the numbers together, and all the variables

12g^2-19g=0

a = 12; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·12·0
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{-(-19)-19}{2*12}=\frac{0}{24}
=0
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*12}=\frac{38}{24}
=1+7/12
$