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5/6k+8=-8+1/4k
We move all terms to the left:
5/6k+8-(-8+1/4k)=0
Domain of the equation: 6k!=0
k!=0/6
k!=0
k∈R
Domain of the equation: 4k)!=0We add all the numbers together, and all the variables
k!=0/1
k!=0
k∈R
5/6k-(1/4k-8)+8=0
We get rid of parentheses
5/6k-1/4k+8+8=0
We calculate fractions
20k/24k^2+(-6k)/24k^2+8+8=0
We add all the numbers together, and all the variables
20k/24k^2+(-6k)/24k^2+16=0
We multiply all the terms by the denominator
20k+(-6k)+16*24k^2=0
Wy multiply elements
384k^2+20k+(-6k)=0
We get rid of parentheses
384k^2+20k-6k=0
We add all the numbers together, and all the variables
384k^2+14k=0
a = 384; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·384·0
Δ = 196
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{196}=14$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*384}=\frac{-28}{768} =-7/192 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*384}=\frac{0}{768} =0 $
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