8-3/8k=4k

Solution for 8-3/8k=4k equation:

8-3/8k=4k

We move all terms to the left:

8-3/8k-(4k)=0


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R


We add all the numbers together, and all the variables

-4k-3/8k+8=0

We multiply all the terms by the denominator


-4k*8k+8*8k-3=0

Wy multiply elements

-32k^2+64k-3=0

a = -32; b = 64; c = -3;
Δ = b2-4ac
Δ = 642-4·(-32)·(-3)
Δ = 3712
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:

$\sqrt{\Delta}=\sqrt{3712}=\sqrt{64*58}=\sqrt{64}*\sqrt{58}=8\sqrt{58}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{58}}{2*-32}=\frac{-64-8\sqrt{58}}{-64}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{58}}{2*-32}=\frac{-64+8\sqrt{58}}{-64}
$