1/4k-16=12k

Solution for 1/4k-16=12k equation:

1/4k-16=12k

We move all terms to the left:

1/4k-16-(12k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R


We add all the numbers together, and all the variables

-12k+1/4k-16=0

We multiply all the terms by the denominator


-12k*4k-16*4k+1=0

Wy multiply elements

-48k^2-64k+1=0

a = -48; b = -64; c = +1;
Δ = b2-4ac
Δ = -642-4·(-48)·1
Δ = 4288
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:

$\sqrt{\Delta}=\sqrt{4288}=\sqrt{64*67}=\sqrt{64}*\sqrt{67}=8\sqrt{67}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{67}}{2*-48}=\frac{64-8\sqrt{67}}{-96}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{67}}{2*-48}=\frac{64+8\sqrt{67}}{-96}
$