X=y/3y+6

Solution for X=y/3y+6 equation:

X=X/3X+6

We move all terms to the left:

X-(X/3X+6)=0


Domain of the equation: 3X+6)!=0

X∈R


We get rid of parentheses

X-X/3X-6=0

We multiply all the terms by the denominator


X*3X-X-6*3X=0

We add all the numbers together, and all the variables

-1X+X*3X-6*3X=0

Wy multiply elements

3X^2-1X-18X=0

We add all the numbers together, and all the variables

3X^2-19X=0

a = 3; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·3·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*3}=\frac{38}{6}
=6+1/3
$