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9x/32x+16=1/x
We move all terms to the left:
9x/32x+16-(1/x)=0
Domain of the equation: 32x!=0
x!=0/32
x!=0
x∈R
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
9x/32x-(+1/x)+16=0
We get rid of parentheses
9x/32x-1/x+16=0
We calculate fractions
9x^2/32x^2+(-32x)/32x^2+16=0
We multiply all the terms by the denominator
9x^2+(-32x)+16*32x^2=0
Wy multiply elements
9x^2+512x^2+(-32x)=0
We get rid of parentheses
9x^2+512x^2-32x=0
We add all the numbers together, and all the variables
521x^2-32x=0
a = 521; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·521·0
Δ = 1024
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{1024}=32$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*521}=\frac{0}{1042} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*521}=\frac{64}{1042} =32/521 $
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