(6y-1/y)-2=3

Solution for (6y-1/y)-2=3 equation:

(6y-1/y)-2=3

We move all terms to the left:

(6y-1/y)-2-(3)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+6y-1/y)-2-3=0

We add all the numbers together, and all the variables

(+6y-1/y)-5=0

We get rid of parentheses

6y-1/y-5=0

We multiply all the terms by the denominator


6y*y-5*y-1=0

We add all the numbers together, and all the variables

-5y+6y*y-1=0

Wy multiply elements

6y^2-5y-1=0

a = 6; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·6·(-1)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*6}=\frac{-2}{12}
=-1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*6}=\frac{12}{12}
=1
$