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-2)!=0

X∈R


We get rid of parentheses

X-1/3X+2=0

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 = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*3}=\frac{-6-4\sqrt{3}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*3}=\frac{-6+4\sqrt{3}}{6}
$