1/2k-6=4k-8

Solution for 1/2k-6=4k-8 equation:

1/2k-6=4k-8

We move all terms to the left:

1/2k-6-(4k-8)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We get rid of parentheses

1/2k-4k+8-6=0

We multiply all the terms by the denominator


-4k*2k+8*2k-6*2k+1=0

Wy multiply elements

-8k^2+16k-12k+1=0

We add all the numbers together, and all the variables

-8k^2+4k+1=0

a = -8; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-8)·1
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{3}}{2*-8}=\frac{-4-4\sqrt{3}}{-16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{3}}{2*-8}=\frac{-4+4\sqrt{3}}{-16}
$