X=12y/y-1

Solution for X=12y/y-1 equation:

X=12X/X-1

We move all terms to the left:

X-(12X/X-1)=0


Domain of the equation: X-1)!=0

X∈R


We get rid of parentheses

X-12X/X+1=0

We multiply all the terms by the denominator


X*X-12X+1*X=0

We add all the numbers together, and all the variables

-11X+X*X=0

Wy multiply elements

X^2-11X=0

a = 1; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·1·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*1}=\frac{22}{2}
=11
$