X=3y/y+2

Solution for X=3y/y+2 equation:

X=3X/X+2

We move all terms to the left:

X-(3X/X+2)=0


Domain of the equation: X+2)!=0

X∈R


We get rid of parentheses

X-3X/X-2=0

We multiply all the terms by the denominator


X*X-3X-2*X=0

We add all the numbers together, and all the variables

-5X+X*X=0

Wy multiply elements

X^2-5X=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$