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

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

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

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We get rid of parentheses

-4/3y+7/2y+3=0

We calculate fractions


(-8y)/6y^2+21y/6y^2+3=0

We multiply all the terms by the denominator


(-8y)+21y+3*6y^2=0

We add all the numbers together, and all the variables

21y+(-8y)+3*6y^2=0

Wy multiply elements

18y^2+21y+(-8y)=0

We get rid of parentheses

18y^2+21y-8y=0

We add all the numbers together, and all the variables

18y^2+13y=0

a = 18; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·18·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*18}=\frac{-26}{36}
=-13/18
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*18}=\frac{0}{36}
=0
$