4/y+5=5/2y

Solution for 4/y+5=5/2y equation:

4/y+5=5/2y

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

10y^2+8y+(-5y)=0

We get rid of parentheses

10y^2+8y-5y=0

We add all the numbers together, and all the variables

10y^2+3y=0

a = 10; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·10·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*10}=\frac{-6}{20}
=-3/10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*10}=\frac{0}{20}
=0
$