7/2y+1/3=11/4y

Solution for 7/2y+1/3=11/4y equation:

7/2y+1/3=11/4y

We move all terms to the left:

7/2y+1/3-(11/4y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

7/2y-(+11/4y)+1/3=0

We get rid of parentheses

7/2y-11/4y+1/3=0

We calculate fractions


32y^2/72y^2+252y/72y^2+(-198y)/72y^2=0

We multiply all the terms by the denominator


32y^2+252y+(-198y)=0

We get rid of parentheses

32y^2+252y-198y=0

We add all the numbers together, and all the variables

32y^2+54y=0

a = 32; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·32·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*32}=\frac{-108}{64}
=-1+11/16
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*32}=\frac{0}{64}
=0
$