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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


5y*4y-2*4y-1*4y+1=0

Wy multiply elements

20y^2-8y-4y+1=0

We add all the numbers together, and all the variables

20y^2-12y+1=0

a = 20; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·20·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8}{2*20}=\frac{4}{40}
=1/10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8}{2*20}=\frac{20}{40}
=1/2
$