-3g(g-4)=2-3g

Solution for -3g(g-4)=2-3g equation:

-3g(g-4)=2-3g

We move all terms to the left:

-3g(g-4)-(2-3g)=0

We add all the numbers together, and all the variables

-3g(g-4)-(-3g+2)=0

We multiply parentheses

-3g^2+12g-(-3g+2)=0

We get rid of parentheses

-3g^2+12g+3g-2=0

We add all the numbers together, and all the variables

-3g^2+15g-2=0

a = -3; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·(-3)·(-2)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{201}}{2*-3}=\frac{-15-\sqrt{201}}{-6}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{201}}{2*-3}=\frac{-15+\sqrt{201}}{-6}
$