2/3g+1/2g=13

Solution for 2/3g+1/2g=13 equation:

2/3g+1/2g=13

We move all terms to the left:

2/3g+1/2g-(13)=0


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R



Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R


We calculate fractions


4g/6g^2+3g/6g^2-13=0

We multiply all the terms by the denominator


4g+3g-13*6g^2=0

We add all the numbers together, and all the variables

7g-13*6g^2=0

Wy multiply elements

-78g^2+7g=0

a = -78; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-78)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-78}=\frac{-14}{-156}
=7/78
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-78}=\frac{0}{-156}
=0
$