3y+4/y-1=2+7/y-1

Solution for 3y+4/y-1=2+7/y-1 equation:

3y+4/y-1=2+7/y-1

We move all terms to the left:

3y+4/y-1-(2+7/y-1)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: y-1)!=0

y∈R


We add all the numbers together, and all the variables

3y+4/y-(7/y+1)-1=0

We get rid of parentheses

3y+4/y-7/y-1-1=0

We multiply all the terms by the denominator


3y*y-1*y-1*y+4-7=0

We add all the numbers together, and all the variables

-2y+3y*y-3=0

Wy multiply elements

3y^2-2y-3=0

a = 3; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·3·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{10}}{2*3}=\frac{2-2\sqrt{10}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{10}}{2*3}=\frac{2+2\sqrt{10}}{6}
$