5/8y-3=1/4y+2

Solution for 5/8y-3=1/4y+2 equation:

5/8y-3=1/4y+2

We move all terms to the left:

5/8y-3-(1/4y+2)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 4y+2)!=0

y∈R


We get rid of parentheses

5/8y-1/4y-2-3=0

We calculate fractions


20y/32y^2+(-8y)/32y^2-2-3=0

We add all the numbers together, and all the variables

20y/32y^2+(-8y)/32y^2-5=0

We multiply all the terms by the denominator


20y+(-8y)-5*32y^2=0

Wy multiply elements

-160y^2+20y+(-8y)=0

We get rid of parentheses

-160y^2+20y-8y=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{-24}{-320}
=3/40
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-160}=\frac{0}{-320}
=0
$