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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 8y+1)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


8y/32y^2+(-20y)/32y^2-1-2=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-96y^2+8y+(-20y)=0

We get rid of parentheses

-96y^2+8y-20y=0

We add all the numbers together, and all the variables

-96y^2-12y=0

a = -96; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-96)·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*-96}=\frac{0}{-192}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-96}=\frac{24}{-192}
=-1/8
$