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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



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

y∈R


We get rid of parentheses

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

We calculate fractions


6y/128y^2+(-64y)/128y^2+(-2y)/128y^2-2=0

We multiply all the terms by the denominator


6y+(-64y)+(-2y)-2*128y^2=0

Wy multiply elements

-256y^2+6y+(-64y)+(-2y)=0

We get rid of parentheses

-256y^2+6y-64y-2y=0

We add all the numbers together, and all the variables

-256y^2-60y=0

a = -256; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·(-256)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*-256}=\frac{0}{-512}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*-256}=\frac{120}{-512}
=-15/64
$