48/y+9=42/2y

Solution for 48/y+9=42/2y equation:

48/y+9=42/2y

We move all terms to the left:

48/y+9-(42/2y)=0


Domain of the equation: 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

48/y-(+42/2y)+9=0

We get rid of parentheses

48/y-42/2y+9=0

We calculate fractions


96y/2y^2+(-42y)/2y^2+9=0

We multiply all the terms by the denominator


96y+(-42y)+9*2y^2=0

Wy multiply elements

18y^2+96y+(-42y)=0

We get rid of parentheses

18y^2+96y-42y=0

We add all the numbers together, and all the variables

18y^2+54y=0

a = 18; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·18·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*18}=\frac{-108}{36}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*18}=\frac{0}{36}
=0
$