y-2/y+3=6

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

y-2/y+3=6

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y-2/y-3=0

We multiply all the terms by the denominator


y*y-3*y-2=0

We add all the numbers together, and all the variables

-3y+y*y-2=0

Wy multiply elements

y^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}
$