2(y2+1/y2)-6(y+1/y)=4

Solution for 2(y2+1/y2)-6(y+1/y)=4 equation:

2(y2+1/y2)-6(y+1/y)=4

We move all terms to the left:

2(y2+1/y2)-6(y+1/y)-(4)=0


Domain of the equation: y2)!=0

y!=0/1

y!=0

y∈R



Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2(+y^2+1/y2)-6(+y+1/y)-4=0

We multiply parentheses

2y^2+2y-6y-6y-4=0

We add all the numbers together, and all the variables

2y^2-10y-4=0

a = 2; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·2·(-4)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{33}}{2*2}=\frac{10-2\sqrt{33}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{33}}{2*2}=\frac{10+2\sqrt{33}}{4}
$