Y=x-1/x+2

Solution for Y=x-1/x+2 equation:

=Y-1/Y+2

We move all terms to the left:

-(Y-1/Y+2)=0


Domain of the equation: Y+2)!=0

Y∈R


We get rid of parentheses

-Y+1/Y-2=0

We multiply all the terms by the denominator


-Y*Y-2*Y+1=0

We add all the numbers together, and all the variables

-2Y-Y*Y+1=0

Wy multiply elements

-1Y^2-2Y+1=0

a = -1; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-1)·1
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{2}}{2*-1}=\frac{2-2\sqrt{2}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{2}}{2*-1}=\frac{2+2\sqrt{2}}{-2}
$