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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



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

y∈R


We get rid of parentheses

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

We calculate fractions


12y/8y^2+(-2y)/8y^2-2-8=0

We add all the numbers together, and all the variables

12y/8y^2+(-2y)/8y^2-10=0

We multiply all the terms by the denominator


12y+(-2y)-10*8y^2=0

Wy multiply elements

-80y^2+12y+(-2y)=0

We get rid of parentheses

-80y^2+12y-2y=0

We add all the numbers together, and all the variables

-80y^2+10y=0

a = -80; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-80)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-80}=\frac{-20}{-160}
=1/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-80}=\frac{0}{-160}
=0
$