X+2=1/6y

Solution for X+2=1/6y equation:

X+2=1/6X

We move all terms to the left:

X+2-(1/6X)=0


Domain of the equation: 6X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1/6X)+2=0

We get rid of parentheses

X-1/6X+2=0

We multiply all the terms by the denominator


X*6X+2*6X-1=0

Wy multiply elements

6X^2+12X-1=0

a = 6; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·6·(-1)
Δ = 168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*6}=\frac{-12-2\sqrt{42}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*6}=\frac{-12+2\sqrt{42}}{12}
$