2/3y-7=1/4y+1

Solution for 2/3y-7=1/4y+1 equation:

2/3y-7=1/4y+1

We move all terms to the left:

2/3y-7-(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

2/3y-1/4y-1-7=0

We calculate fractions


8y/12y^2+(-3y)/12y^2-1-7=0

We add all the numbers together, and all the variables

8y/12y^2+(-3y)/12y^2-8=0

We multiply all the terms by the denominator


8y+(-3y)-8*12y^2=0

Wy multiply elements

-96y^2+8y+(-3y)=0

We get rid of parentheses

-96y^2+8y-3y=0

We add all the numbers together, and all the variables

-96y^2+5y=0

a = -96; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-96)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-96}=\frac{-10}{-192}
=5/96
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-96}=\frac{0}{-192}
=0
$