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

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

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

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


32y^2/72y^2+396y/72y^2+(-126y)/72y^2=0

We multiply all the terms by the denominator


32y^2+396y+(-126y)=0

We get rid of parentheses

32y^2+396y-126y=0

We add all the numbers together, and all the variables

32y^2+270y=0

a = 32; b = 270; c = 0;
Δ = b2-4ac
Δ = 2702-4·32·0
Δ = 72900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{72900}=270$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-270}{2*32}=\frac{-540}{64}
=-8+7/16
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+270}{2*32}=\frac{0}{64}
=0
$