2/3g+g=-12

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

2/3g+g=-12

We move all terms to the left:

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


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R


We add all the numbers together, and all the variables

g+2/3g+12=0

We multiply all the terms by the denominator


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

Wy multiply elements

3g^2+36g+2=0

a = 3; b = 36; c = +2;
Δ = b2-4ac
Δ = 362-4·3·2
Δ = 1272
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:

$\sqrt{\Delta}=\sqrt{1272}=\sqrt{4*318}=\sqrt{4}*\sqrt{318}=2\sqrt{318}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{318}}{2*3}=\frac{-36-2\sqrt{318}}{6}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{318}}{2*3}=\frac{-36+2\sqrt{318}}{6}
$