2/3g+1/4g=14

Solution for 2/3g+1/4g=14 equation:

2/3g+1/4g=14

We move all terms to the left:

2/3g+1/4g-(14)=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^2-14=0

We multiply all the terms by the denominator


8g+3g-14*12g^2=0

We add all the numbers together, and all the variables

11g-14*12g^2=0

Wy multiply elements

-168g^2+11g=0

a = -168; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-168)·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*-168}=\frac{-22}{-336}
=11/168
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-168}=\frac{0}{-336}
=0
$