1+9/4y=1/8y

Solution for 1+9/4y=1/8y equation:

1+9/4y=1/8y

We move all terms to the left:

1+9/4y-(1/8y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 8y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

9/4y-(+1/8y)+1=0

We get rid of parentheses

9/4y-1/8y+1=0

We calculate fractions


72y/32y^2+(-4y)/32y^2+1=0

We multiply all the terms by the denominator


72y+(-4y)+1*32y^2=0

Wy multiply elements

32y^2+72y+(-4y)=0

We get rid of parentheses

32y^2+72y-4y=0

We add all the numbers together, and all the variables

32y^2+68y=0

a = 32; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·32·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*32}=\frac{-136}{64}
=-2+1/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*32}=\frac{0}{64}
=0
$