1/6g+3=4-1/3g

Solution for 1/6g+3=4-1/3g equation:

1/6g+3=4-1/3g

We move all terms to the left:

1/6g+3-(4-1/3g)=0


Domain of the equation: 6g!=0

g!=0/6

g!=0

g∈R



Domain of the equation: 3g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

1/6g-(-1/3g+4)+3=0

We get rid of parentheses

1/6g+1/3g-4+3=0

We calculate fractions


3g/18g^2+6g/18g^2-4+3=0

We add all the numbers together, and all the variables

3g/18g^2+6g/18g^2-1=0

We multiply all the terms by the denominator


3g+6g-1*18g^2=0

We add all the numbers together, and all the variables

9g-1*18g^2=0

Wy multiply elements

-18g^2+9g=0

a = -18; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-18)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-18}=\frac{-18}{-36}
=1/2
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-18}=\frac{0}{-36}
=0
$