-7/3y-7/4=3/4y-1

Solution for -7/3y-7/4=3/4y-1 equation:

-7/3y-7/4=3/4y-1

We move all terms to the left:

-7/3y-7/4-(3/4y-1)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y-1)!=0

y∈R


We get rid of parentheses

-7/3y-3/4y+1-7/4=0

We calculate fractions


(-448y)/192y^2+(-9y)/192y^2+(-21y)/192y^2+1=0

We multiply all the terms by the denominator


(-448y)+(-9y)+(-21y)+1*192y^2=0

Wy multiply elements

192y^2+(-448y)+(-9y)+(-21y)=0

We get rid of parentheses

192y^2-448y-9y-21y=0

We add all the numbers together, and all the variables

192y^2-478y=0

a = 192; b = -478; c = 0;
Δ = b2-4ac
Δ = -4782-4·192·0
Δ = 228484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{228484}=478$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-478)-478}{2*192}=\frac{0}{384}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-478)+478}{2*192}=\frac{956}{384}
=2+47/96
$