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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y-1)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


9y/192y^2+128y/192y^2+(-9y)/192y^2+1=0

We multiply all the terms by the denominator


9y+128y+(-9y)+1*192y^2=0

We add all the numbers together, and all the variables

137y+(-9y)+1*192y^2=0

Wy multiply elements

192y^2+137y+(-9y)=0

We get rid of parentheses

192y^2+137y-9y=0

We add all the numbers together, and all the variables

192y^2+128y=0

a = 192; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·192·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*192}=\frac{-256}{384}
=-2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*192}=\frac{0}{384}
=0
$