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

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

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

We move all terms to the left:

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


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3y/4+1y/2y-3-2=0

We calculate fractions


6y^2/8y+4y/8y-3-2=0

We add all the numbers together, and all the variables

6y^2/8y+4y/8y-5=0

We multiply all the terms by the denominator


6y^2+4y-5*8y=0

Wy multiply elements

6y^2+4y-40y=0

We add all the numbers together, and all the variables

6y^2-36y=0

a = 6; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·6·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*6}=\frac{0}{12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*6}=\frac{72}{12}
=6
$