3/4y-6=2+1/2y

Solution for 3/4y-6=2+1/2y equation:

3/4y-6=2+1/2y

We move all terms to the left:

3/4y-6-(2+1/2y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y-(1/2y+2)-6=0

We get rid of parentheses

3/4y-1/2y-2-6=0

We calculate fractions


6y/8y^2+(-4y)/8y^2-2-6=0

We add all the numbers together, and all the variables

6y/8y^2+(-4y)/8y^2-8=0

We multiply all the terms by the denominator


6y+(-4y)-8*8y^2=0

Wy multiply elements

-64y^2+6y+(-4y)=0

We get rid of parentheses

-64y^2+6y-4y=0

We add all the numbers together, and all the variables

-64y^2+2y=0

a = -64; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-64)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-64}=\frac{-4}{-128}
=1/32
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-64}=\frac{0}{-128}
=0
$