3/8y=3/4y+5

Solution for 3/8y=3/4y+5 equation:

3/8y=3/4y+5

We move all terms to the left:

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


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 4y+5)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


12y/32y^2+(-24y)/32y^2-5=0

We multiply all the terms by the denominator


12y+(-24y)-5*32y^2=0

Wy multiply elements

-160y^2+12y+(-24y)=0

We get rid of parentheses

-160y^2+12y-24y=0

We add all the numbers together, and all the variables

-160y^2-12y=0

a = -160; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-160)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-160}=\frac{0}{-320}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-160}=\frac{24}{-320}
=-3/40
$