32-3/8y=3/4y-14

Solution for 32-3/8y=3/4y-14 equation:

32-3/8y=3/4y-14

We move all terms to the left:

32-3/8y-(3/4y-14)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 4y-14)!=0

y∈R


We get rid of parentheses

-3/8y-3/4y+14+32=0

We calculate fractions


(-12y)/32y^2+(-24y)/32y^2+14+32=0

We add all the numbers together, and all the variables

(-12y)/32y^2+(-24y)/32y^2+46=0

We multiply all the terms by the denominator


(-12y)+(-24y)+46*32y^2=0

Wy multiply elements

1472y^2+(-12y)+(-24y)=0

We get rid of parentheses

1472y^2-12y-24y=0

We add all the numbers together, and all the variables

1472y^2-36y=0

a = 1472; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·1472·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*1472}=\frac{0}{2944}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*1472}=\frac{72}{2944}
=9/368
$