The difference of a number and 2 times its reciprocal is 17 over 4. what is the number

I neeeeed your answers asap.

Say, aren't you from dominican school?

Let the number be x and reciprocal 1/x

=> x - 2/x = 17/4

=> x² - 2 = 17x/4

i.e. 4x² - 17x - 8 = 0

Using the quadratic formula we have:

x = (17 ± √((17)²+ 4(4)(8))/8

=> x = [17 ± √(289 + 128)]/8

=> x = [17 ± √417]/8

so, x = 4.68 or x = -0.43

:)>

x -2/x = 17/4
multiply with x:
x^2 -2 = 17/4 x
move to one side:
x^2 -17/4 x - 2 = 0

formula for quadratic equations => x=(17/4 +/- sqrt(289/16 + 4*2)/2 =
= 17/8 +/- sqrt(417/16)/2 =
= 17/8 +/- sqrt(417/(16*4)) =
= 17/8 +/- sqrt(417)/sqrt(64) = 17/8 +/- sqrt(417)/8

so x1 = 17/8 + sqrt(417)/8
x2 = 17/8 - sqrt(417)/8

a - 2/a = 17/4

Two possible answers (used a calc. to solve)

a = [17 - root(417)] / 8
a = [17 + root(417)] / 8

a - 2/a = 17/4
4a^2 - 17 a -8 = 0
Use the quadratic formula,
a = [ 17 + sqrt(417) ] / 8
a = [ 17 - sqrt(417) ] / 8

(x - 2/x) = 17/4
x^2 -2 = x17/4
4x^2 -8 - 17x = 0
4x^2 -17x - 8 = 0
x = {17 +/- sqrt (289 +128)}/8
x = {17 +/ - sqrt(417)}/8

x - 2/x = 17/4
4x² - 8 = 17x
4x² - 17x - 8 = 0
This does not lead to whole number solution.