1/2k-5=k-1

Solution for 1/2k-5=k-1 equation:

1/2k-5=k-1

We move all terms to the left:

1/2k-5-(k-1)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-2k^2+2k-10k+1=0

We add all the numbers together, and all the variables

-2k^2-8k+1=0

a = -2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-2)·1
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{2}}{2*-2}=\frac{8-6\sqrt{2}}{-4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*-2}=\frac{8+6\sqrt{2}}{-4}
$