4/y-5=9/2y

Solution for 4/y-5=9/2y equation:

4/y-5=9/2y

We move all terms to the left:

4/y-5-(9/2y)=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

4/y-(+9/2y)-5=0

We get rid of parentheses

4/y-9/2y-5=0

We calculate fractions


8y/2y^2+(-9y)/2y^2-5=0

We multiply all the terms by the denominator


8y+(-9y)-5*2y^2=0

Wy multiply elements

-10y^2+8y+(-9y)=0

We get rid of parentheses

-10y^2+8y-9y=0

We add all the numbers together, and all the variables

-10y^2-1y=0

a = -10; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-10)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-10}=\frac{0}{-20}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-10}=\frac{2}{-20}
=-1/10
$