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2-3/4k=1/8k+19
We move all terms to the left:
2-3/4k-(1/8k+19)=0
Domain of the equation: 4k!=0
k!=0/4
k!=0
k∈R
Domain of the equation: 8k+19)!=0We get rid of parentheses
k∈R
-3/4k-1/8k-19+2=0
We calculate fractions
(-24k)/32k^2+(-4k)/32k^2-19+2=0
We add all the numbers together, and all the variables
(-24k)/32k^2+(-4k)/32k^2-17=0
We multiply all the terms by the denominator
(-24k)+(-4k)-17*32k^2=0
Wy multiply elements
-544k^2+(-24k)+(-4k)=0
We get rid of parentheses
-544k^2-24k-4k=0
We add all the numbers together, and all the variables
-544k^2-28k=0
a = -544; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-544)·0
Δ = 784
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{784}=28$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*-544}=\frac{0}{-1088} =0 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-544}=\frac{56}{-1088} =-7/136 $
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