8k-5=1/4k=1

Solution for 8k-5=1/4k=1 equation:

8k-5=1/4k=1

We move all terms to the left:

8k-5-(1/4k)=0


Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

8k-(+1/4k)-5=0

We get rid of parentheses

8k-1/4k-5=0

We multiply all the terms by the denominator


8k*4k-5*4k-1=0

Wy multiply elements

32k^2-20k-1=0

a = 32; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·32·(-1)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{33}}{2*32}=\frac{20-4\sqrt{33}}{64}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{33}}{2*32}=\frac{20+4\sqrt{33}}{64}
$