X-(1/3y)=-1

Solution for X-(1/3y)=-1 equation:

X-(1/3X)=-1

We move all terms to the left:

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


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

X-1/3X+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

3X^2+3X-1=0

a = 3; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·3·(-1)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{21}}{2*3}=\frac{-3-\sqrt{21}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{21}}{2*3}=\frac{-3+\sqrt{21}}{6}
$