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

Solution for (4/y)-(5/2y)=5 equation:

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

We move all terms to the left:

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


Domain of the equation: y)!=0

y!=0/1

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
$