24/5y+4=4/y-1

Solution for 24/5y+4=4/y-1 equation:

24/5y+4=4/y-1

We move all terms to the left:

24/5y+4-(4/y-1)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: y-1)!=0

y∈R


We get rid of parentheses

24/5y-4/y+1+4=0

We calculate fractions


24y/5y^2+(-20y)/5y^2+1+4=0

We add all the numbers together, and all the variables

24y/5y^2+(-20y)/5y^2+5=0

We multiply all the terms by the denominator


24y+(-20y)+5*5y^2=0

Wy multiply elements

25y^2+24y+(-20y)=0

We get rid of parentheses

25y^2+24y-20y=0

We add all the numbers together, and all the variables

25y^2+4y=0

a = 25; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·25·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*25}=\frac{-8}{50}
=-4/25
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*25}=\frac{0}{50}
=0
$