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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 2+4y-3)!=0

We move all terms containing y to the left, all other terms to the right

4y-3)!=-2

y∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2y-4y+6y/8y+(-4y)/8y+3=0

We add all the numbers together, and all the variables

-2y+6y/8y+(-4y)/8y+3=0

We multiply all the terms by the denominator


-2y*8y+6y+(-4y)+3*8y=0

We add all the numbers together, and all the variables

6y-2y*8y+(-4y)+3*8y=0

Wy multiply elements

-16y^2+6y+(-4y)+24y=0

We get rid of parentheses

-16y^2+6y-4y+24y=0

We add all the numbers together, and all the variables

-16y^2+26y=0

a = -16; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-16)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-16}=\frac{-52}{-32}
=1+5/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-16}=\frac{0}{-32}
=0
$