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

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

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

We move all terms to the left:

-1/3y-3/4-(1/4y-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

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

We calculate fractions


(-64y)/192y^2+(-3y)/192y^2+(-9y)/192y^2+1=0

We multiply all the terms by the denominator


(-64y)+(-3y)+(-9y)+1*192y^2=0

Wy multiply elements

192y^2+(-64y)+(-3y)+(-9y)=0

We get rid of parentheses

192y^2-64y-3y-9y=0

We add all the numbers together, and all the variables

192y^2-76y=0

a = 192; b = -76; c = 0;
Δ = b2-4ac
Δ = -762-4·192·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-76}{2*192}=\frac{0}{384}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+76}{2*192}=\frac{152}{384}
=19/48
$