X+1/3y=2

Solution for X+1/3y=2 equation:

X+1/3X=2

We move all terms to the left:

X+1/3X-(2)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-2*3X+1=0

Wy multiply elements

3X^2-6X+1=0

a = 3; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·3·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{6}}{2*3}=\frac{6-2\sqrt{6}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{6}}{2*3}=\frac{6+2\sqrt{6}}{6}
$