(5/6)k=1/6

Solution for (5/6)k=1/6 equation:

(5/6)k=1/6

We move all terms to the left:

(5/6)k-(1/6)=0


Domain of the equation: 6)k!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

(+5/6)k-(+1/6)=0

We multiply parentheses

5k^2-(+1/6)=0

We get rid of parentheses

5k^2-1/6=0

We multiply all the terms by the denominator


5k^2*6-1=0

Wy multiply elements

30k^2-1=0

a = 30; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·30·(-1)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*30}=\frac{0-2\sqrt{30}}{60}
=-\frac{2\sqrt{30}}{60}
=-\frac{\sqrt{30}}{30}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*30}=\frac{0+2\sqrt{30}}{60}
=\frac{2\sqrt{30}}{60}
=\frac{\sqrt{30}}{30}
$