y+1/y=12

Solution for y+1/y=12 equation:

y+1/y=12

We move all terms to the left:

y+1/y-(12)=0


Domain of the equation: y!=0

y∈R


We multiply all the terms by the denominator


y*y-12*y+1=0

We add all the numbers together, and all the variables

-12y+y*y+1=0

Wy multiply elements

y^2-12y+1=0

a = 1; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·1·1
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{35}}{2*1}=\frac{12-2\sqrt{35}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{35}}{2*1}=\frac{12+2\sqrt{35}}{2}
$