Y=x-2/x+4

Solution for Y=x-2/x+4 equation:

=Y-2/Y+4

We move all terms to the left:

-(Y-2/Y+4)=0


Domain of the equation: Y+4)!=0

Y∈R


We get rid of parentheses

-Y+2/Y-4=0

We multiply all the terms by the denominator


-Y*Y-4*Y+2=0

We add all the numbers together, and all the variables

-4Y-Y*Y+2=0

Wy multiply elements

-1Y^2-4Y+2=0

a = -1; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-1)·2
Δ = 24
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:

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