5/8k-1/4k=1

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

5/8k-1/4k=1

We move all terms to the left:

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


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R



Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R


We calculate fractions


20k/32k^2+(-8k)/32k^2-1=0

We multiply all the terms by the denominator


20k+(-8k)-1*32k^2=0

Wy multiply elements

-32k^2+20k+(-8k)=0

We get rid of parentheses

-32k^2+20k-8k=0

We add all the numbers together, and all the variables

-32k^2+12k=0

a = -32; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-32)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-32}=\frac{-24}{-64}
=3/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-32}=\frac{0}{-64}
=0
$