4/3g+1/6g=3/2

Solution for 4/3g+1/6g=3/2 equation:

4/3g+1/6g=3/2

We move all terms to the left:

4/3g+1/6g-(3/2)=0


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R



Domain of the equation: 6g!=0

g!=0/6

g!=0

g∈R


We add all the numbers together, and all the variables

4/3g+1/6g-(+3/2)=0

We get rid of parentheses

4/3g+1/6g-3/2=0

We calculate fractions


(-324g^2)/72g^2+96g/72g^2+12g/72g^2=0

We multiply all the terms by the denominator


(-324g^2)+96g+12g=0

We add all the numbers together, and all the variables

(-324g^2)+108g=0

We get rid of parentheses

-324g^2+108g=0

a = -324; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-324)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-324}=\frac{-216}{-648}
=1/3
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-324}=\frac{0}{-648}
=0
$