factor this quadratic equation and solve for x?

Question

3/x = x + 5/2 ( the x + 5 is all over 2)

Answer 1

Let say x is y, to avoid any confusion.
3/y = (y + 5)/2

Multiply by 2 at both side.
3/y x 2 = (y + 5)/2 x 2
6/y = y + 5

Multiply by y at both side.
6/y x y = y x (y + 5)
6 = y(y + 5)
6 = y^2 + 5y

Bring all the numbers to one side.
y^2 + 5y - 6 = 0

Factorize the equation.
(y + 6)(y - 1) = 0

Therefore,
y + 6 = 0 or y - 1 = 0
y = -6 or y = 1

In short,
y = -6, 1

As I had mentioned earlier, x = y.
Therefore, x = -6, 1.

Answer 2

3/x = (x+5)/2
= 6 = x^2 + 5x
= x^2 + 5x - 6 = 0
= x^2 + 6x - x - 6 = 0
= x(x + 6) - 1(x + 6)
= (x - 1)(x + 6)

Answer 3

so 3 = (x^2+5)/2 or x^2+5x=6 or x^2+5x-6 = 0. so (x+6)(x-1) = 0. So x=1 or x= -6.

Steve

Answer 4

3/x=(x+5)/2 multiply by 2x
6=x(x+5)=x^2+5x subtract 6
x^2+5x-6=0
(x+6)(x-1)=0
x=-6
x=1

roots are x=-6, 1