2/3g+1/4g=22

Solution for 2/3g+1/4g=22 equation:

2/3g+1/4g=22

We move all terms to the left:

2/3g+1/4g-(22)=0


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R



Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R


We calculate fractions


8g/12g^2+3g/12g^2-22=0

We multiply all the terms by the denominator


8g+3g-22*12g^2=0

We add all the numbers together, and all the variables

11g-22*12g^2=0

Wy multiply elements

-264g^2+11g=0

a = -264; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-264)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-264}=\frac{-22}{-528}
=1/24
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-264}=\frac{0}{-528}
=0
$