Question 548893
Let x be the number
Reciprocal of x = 1/x
Twice the x = 2x

{{{2x-1/x=7/2}}}
Multiply by x both sides
{{{x(2x-1/x)=x(7/2)}}}
{{{2x^2-1=7x/2}}}
Multiply by 2 both sides
{{{2(2x^2-1)=2(7x/2)}}}
{{{4x^2-2=cross(2)(7x/cross(2))}}}
{{{4x^2-2=7x}}}
{{{4x^2-7x-2=0}}}
Solve for x
{{{4x^2-8x+x-2=0}}}
{{{4x(x-2)+1(x-2)=0}}}
{{{(x-2)(4x+1)=0}}}
{{{x-2=0}}} or {{{4x+1=0}}}
{{{x=2}}} or {{{4x=-1}}}
{{{x=2}}} or {{{x=-1/4}}}



Now check which value of x satisfies given condition

{{{2x-1/x=7/2}}}
Put x = -1/4
{{{2(-1/4)-1/(-1/4)=7/2}}}
{{{-1/2-(-4)=7/2}}}
{{{(-1/2)+4=7/2}}}
{{{(-1+8)/2=7/2}}}
{{{7/2=7/2}}}



{{{2x-1/x=7/2}}}
Put x = 2
{{{2(2)-1/2=7/2}}}
{{{4-1/2=7/2}}}
{{{(8-1)/2=7/2}}}
{{{7/2=7/2}}}

Both values of x satisfy the given condition
Therefore x=2 or x=-1/4