0/1=5k-5/k+1

Solution for 0/1=5k-5/k+1 equation:

0/1=5k-5/k+1

We move all terms to the left:

0/1-(5k-5/k+1)=0


Domain of the equation: k+1)!=0

k∈R


We add all the numbers together, and all the variables

-(5k-5/k+1)=0

We get rid of parentheses

-5k+5/k-1=0

We multiply all the terms by the denominator


-5k*k-1*k+5=0

We add all the numbers together, and all the variables

-1k-5k*k+5=0

Wy multiply elements

-5k^2-1k+5=0

a = -5; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-5)·5
Δ = 101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{101}}{2*-5}=\frac{1-\sqrt{101}}{-10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{101}}{2*-5}=\frac{1+\sqrt{101}}{-10}
$