y=2y-5/y+2

Solution for y=2y-5/y+2 equation:

y=2y-5/y+2

We move all terms to the left:

y-(2y-5/y+2)=0


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

y∈R


We get rid of parentheses

y-2y+5/y-2=0

We multiply all the terms by the denominator


y*y-2y*y-2*y+5=0

We add all the numbers together, and all the variables

-2y+y*y-2y*y+5=0

Wy multiply elements

y^2-2y^2-2y+5=0

We add all the numbers together, and all the variables

-1y^2-2y+5=0

a = -1; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-1)·5
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{-(-2)-2\sqrt{6}}{2*-1}=\frac{2-2\sqrt{6}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*-1}=\frac{2+2\sqrt{6}}{-2}
$