5y-5/y=5

Solution for 5y-5/y=5 equation:

5y-5/y=5

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R


We multiply all the terms by the denominator


5y*y-5*y-5=0

We add all the numbers together, and all the variables

-5y+5y*y-5=0

Wy multiply elements

5y^2-5y-5=0

a = 5; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·5·(-5)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{5}}{2*5}=\frac{5-5\sqrt{5}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{5}}{2*5}=\frac{5+5\sqrt{5}}{10}
$