2-3/4y=5/8y

Solution for 2-3/4y=5/8y equation:

2-3/4y=5/8y

We move all terms to the left:

2-3/4y-(5/8y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 8y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-3/4y-(+5/8y)+2=0

We get rid of parentheses

-3/4y-5/8y+2=0

We calculate fractions


(-24y)/32y^2+(-20y)/32y^2+2=0

We multiply all the terms by the denominator


(-24y)+(-20y)+2*32y^2=0

Wy multiply elements

64y^2+(-24y)+(-20y)=0

We get rid of parentheses

64y^2-24y-20y=0

We add all the numbers together, and all the variables

64y^2-44y=0

a = 64; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·64·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*64}=\frac{0}{128}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*64}=\frac{88}{128}
=11/16
$