y+2=14/y

Solution for y+2=14/y equation:

y+2=14/y

We move all terms to the left:

y+2-(14/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(+14/y)+2=0

We get rid of parentheses

y-14/y+2=0

We multiply all the terms by the denominator


y*y+2*y-14=0

We add all the numbers together, and all the variables

2y+y*y-14=0

Wy multiply elements

y^2+2y-14=0

a = 1; b = 2; c = -14;
Δ = b2-4ac
Δ = 22-4·1·(-14)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{15}}{2*1}=\frac{-2-2\sqrt{15}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{15}}{2*1}=\frac{-2+2\sqrt{15}}{2}
$