2y/y+3y=4

Solution for 2y/y+3y=4 equation:

2y/y+3y=4

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

3y+2y/y-4=0

We multiply all the terms by the denominator


3y*y+2y-4*y=0

We add all the numbers together, and all the variables

-2y+3y*y=0

Wy multiply elements

3y^2-2y=0

a = 3; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·3·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*3}=\frac{0}{6}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*3}=\frac{4}{6}
=2/3
$