2/3g+1/9g=14

Solution for 2/3g+1/9g=14 equation:

2/3g+1/9g=14

We move all terms to the left:

2/3g+1/9g-(14)=0


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R



Domain of the equation: 9g!=0

g!=0/9

g!=0

g∈R


We calculate fractions


18g/27g^2+3g/27g^2-14=0

We multiply all the terms by the denominator


18g+3g-14*27g^2=0

We add all the numbers together, and all the variables

21g-14*27g^2=0

Wy multiply elements

-378g^2+21g=0

a = -378; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-378)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-378}=\frac{-42}{-756}
=1/18
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-378}=\frac{0}{-756}
=0
$