5-g=2/3g

Solution for 5-g=2/3g equation:

5-g=2/3g

We move all terms to the left:

5-g-(2/3g)=0


Domain of the equation: 3g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

-g-(+2/3g)+5=0

We add all the numbers together, and all the variables

-1g-(+2/3g)+5=0

We get rid of parentheses

-1g-2/3g+5=0

We multiply all the terms by the denominator


-1g*3g+5*3g-2=0

Wy multiply elements

-3g^2+15g-2=0

a = -3; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·(-3)·(-2)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{201}}{2*-3}=\frac{-15-\sqrt{201}}{-6}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{201}}{2*-3}=\frac{-15+\sqrt{201}}{-6}
$