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1/3k+80=1/8k+120
We move all terms to the left:
1/3k+80-(1/8k+120)=0
Domain of the equation: 3k!=0
k!=0/3
k!=0
k∈R
Domain of the equation: 8k+120)!=0We get rid of parentheses
k∈R
1/3k-1/8k-120+80=0
We calculate fractions
8k/24k^2+(-3k)/24k^2-120+80=0
We add all the numbers together, and all the variables
8k/24k^2+(-3k)/24k^2-40=0
We multiply all the terms by the denominator
8k+(-3k)-40*24k^2=0
Wy multiply elements
-960k^2+8k+(-3k)=0
We get rid of parentheses
-960k^2+8k-3k=0
We add all the numbers together, and all the variables
-960k^2+5k=0
a = -960; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-960)·0
Δ = 25
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{25}=5k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-960}=\frac{-10}{-1920} =1/192k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-960}=\frac{0}{-1920} =0
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