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1/2x+1/48x=16
We move all terms to the left:
1/2x+1/48x-(16)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 48x!=0We calculate fractions
x!=0/48
x!=0
x∈R
48x/96x^2+2x/96x^2-16=0
We multiply all the terms by the denominator
48x+2x-16*96x^2=0
We add all the numbers together, and all the variables
50x-16*96x^2=0
Wy multiply elements
-1536x^2+50x=0
a = -1536; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-1536)·0
Δ = 2500
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{2500}=50$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-1536}=\frac{-100}{-3072} =25/768 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-1536}=\frac{0}{-3072} =0 $
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