3=y-2/y+6

Solution for 3=y-2/y+6 equation:

3=y-2/y+6

We move all terms to the left:

3-(y-2/y+6)=0


Domain of the equation: y+6)!=0

y∈R


We get rid of parentheses

-y+2/y-6+3=0

We multiply all the terms by the denominator


-y*y-6*y+3*y+2=0

We add all the numbers together, and all the variables

-3y-y*y+2=0

Wy multiply elements

-1y^2-3y+2=0

a = -1; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-1)·2
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{17}}{2*-1}=\frac{3-\sqrt{17}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*-1}=\frac{3+\sqrt{17}}{-2}
$