2y+1/y=8

Solution for 2y+1/y=8 equation:

2y+1/y=8

We move all terms to the left:

2y+1/y-(8)=0


Domain of the equation: y!=0

y∈R


We multiply all the terms by the denominator


2y*y-8*y+1=0

We add all the numbers together, and all the variables

-8y+2y*y+1=0

Wy multiply elements

2y^2-8y+1=0

a = 2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·2·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{14}}{2*2}=\frac{8-2\sqrt{14}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{14}}{2*2}=\frac{8+2\sqrt{14}}{4}
$