3/4y-5=1/8y

Solution for 3/4y-5=1/8y equation:

3/4y-5=1/8y

We move all terms to the left:

3/4y-5-(1/8y)=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-(+1/8y)-5=0

We get rid of parentheses

3/4y-1/8y-5=0

We calculate fractions


24y/32y^2+(-4y)/32y^2-5=0

We multiply all the terms by the denominator


24y+(-4y)-5*32y^2=0

Wy multiply elements

-160y^2+24y+(-4y)=0

We get rid of parentheses

-160y^2+24y-4y=0

We add all the numbers together, and all the variables

-160y^2+20y=0

a = -160; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-160)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-160}=\frac{-40}{-320}
=1/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-160}=\frac{0}{-320}
=0
$