k/4=4k*

Solution for k/4=4k* equation:

k/4=4k*

We move all terms to the left:

k/4-(4k*)=0

We add all the numbers together, and all the variables

k/4-(+4k*)=0

We get rid of parentheses

k/4-4k*=0

We multiply all the terms by the denominator


k-(4k*)*4=0

We add all the numbers together, and all the variables

k-(+4k*)*4=0

We multiply parentheses

-16k^2+k=0

a = -16; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-16)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-16}=\frac{-2}{-32}
=1/16
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-16}=\frac{0}{-32}
=0
$