3/y+2=7/2y

Solution for 3/y+2=7/2y equation:

3/y+2=7/2y

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/y-7/2y+2=0

We calculate fractions


6y/2y^2+(-7y)/2y^2+2=0

We multiply all the terms by the denominator


6y+(-7y)+2*2y^2=0

Wy multiply elements

4y^2+6y+(-7y)=0

We get rid of parentheses

4y^2+6y-7y=0

We add all the numbers together, and all the variables

4y^2-1y=0

a = 4; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·4·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*4}=\frac{0}{8}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*4}=\frac{2}{8}
=1/4
$