.(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∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


.(6y-1)-5*y=0

We add all the numbers together, and all the variables

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

We multiply parentheses

6y^2-5y+=0

We add all the numbers together, and all the variables

6y^2-5y=0

a = 6; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·6·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*6}=\frac{0}{12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*6}=\frac{10}{12}
=5/6
$