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1/2k+6=k-2
We move all terms to the left:
1/2k+6-(k-2)=0
Domain of the equation: 2k!=0We get rid of parentheses
k!=0/2
k!=0
k∈R
1/2k-k+2+6=0
We multiply all the terms by the denominator
-k*2k+2*2k+6*2k+1=0
Wy multiply elements
-2k^2+4k+12k+1=0
We add all the numbers together, and all the variables
-2k^2+16k+1=0
a = -2; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-2)·1
Δ = 264
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{66}}{2*-2}=\frac{-16-2\sqrt{66}}{-4} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{66}}{2*-2}=\frac{-16+2\sqrt{66}}{-4} $
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