12g=2/3g-1)+11

Solution for 12g=2/3g-1)+11 equation:

12g=2/3g-1)+11

We move all terms to the left:

12g-(2/3g-1)+11)=0


Domain of the equation: 3g-1)!=0

g∈R


We add all the numbers together, and all the variables

12g-(2/3g-1)=0

We get rid of parentheses

12g-2/3g+1=0

We multiply all the terms by the denominator


12g*3g+1*3g-2=0

Wy multiply elements

36g^2+3g-2=0

a = 36; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·36·(-2)
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{33}}{2*36}=\frac{-3-3\sqrt{33}}{72}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{33}}{2*36}=\frac{-3+3\sqrt{33}}{72}
$