2-5y-8=9-3/5y

Solution for 2-5y-8=9-3/5y equation:

2-5y-8=9-3/5y

We move all terms to the left:

2-5y-8-(9-3/5y)=0


Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-5y-(-3/5y+9)+2-8=0

We add all the numbers together, and all the variables

-5y-(-3/5y+9)-6=0

We get rid of parentheses

-5y+3/5y-9-6=0

We multiply all the terms by the denominator


-5y*5y-9*5y-6*5y+3=0

Wy multiply elements

-25y^2-45y-30y+3=0

We add all the numbers together, and all the variables

-25y^2-75y+3=0

a = -25; b = -75; c = +3;
Δ = b2-4ac
Δ = -752-4·(-25)·3
Δ = 5925
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5925}=\sqrt{25*237}=\sqrt{25}*\sqrt{237}=5\sqrt{237}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{237}}{2*-25}=\frac{75-5\sqrt{237}}{-50}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{237}}{2*-25}=\frac{75+5\sqrt{237}}{-50}
$