1/2k-6=4k-8

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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} $

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