8k-23/6k=0

Solution for 8k-23/6k=0 equation:

8k-23/6k=0


Domain of the equation: 6k!=0

k!=0/6

k!=0

k∈R


We multiply all the terms by the denominator


8k*6k-23=0

Wy multiply elements

48k^2-23=0

a = 48; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·48·(-23)
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{69}}{2*48}=\frac{0-8\sqrt{69}}{96}
=-\frac{8\sqrt{69}}{96}
=-\frac{\sqrt{69}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{69}}{2*48}=\frac{0+8\sqrt{69}}{96}
=\frac{8\sqrt{69}}{96}
=\frac{\sqrt{69}}{12}
$