2y-2=4y-6/2y

Solution for 2y-2=4y-6/2y equation:

2y-2=4y-6/2y

We move all terms to the left:

2y-2-(4y-6/2y)=0


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4y^2-8y^2-4y+6=0

We add all the numbers together, and all the variables

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

a = -4; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-4)·6
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*-4}=\frac{4-4\sqrt{7}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*-4}=\frac{4+4\sqrt{7}}{-8}
$