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48/x+8*2=12/x*4
We move all terms to the left:
48/x+8*2-(12/x*4)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: x*4)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
48/x-(+12/x*4)+8*2=0
We add all the numbers together, and all the variables
48/x-(+12/x*4)+16=0
We get rid of parentheses
48/x-12/x*4+16=0
We calculate fractions
768x/16x^2+(-12x)/16x^2+16=0
We multiply all the terms by the denominator
768x+(-12x)+16*16x^2=0
Wy multiply elements
256x^2+768x+(-12x)=0
We get rid of parentheses
256x^2+768x-12x=0
We add all the numbers together, and all the variables
256x^2+756x=0
a = 256; b = 756; c = 0;
Δ = b2-4ac
Δ = 7562-4·256·0
Δ = 571536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{571536}=756$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(756)-756}{2*256}=\frac{-1512}{512} =-2+61/64 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(756)+756}{2*256}=\frac{0}{512} =0 $
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