5k-5/k+1=0

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

5k-5/k+1=0


Domain of the equation: k!=0

k∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

k+5k*k-5=0

Wy multiply elements

5k^2+k-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}
$