2x/(x+3) - x/(x-3) = 5x+2/(x+3)

2x/(x+3) - x/(x-3) = 5x+2/(x+3) solve using quadratic formula?
Please help me with the steps on solving this one with quadratic formula...
The answer is x= 1 +/- √7/2
I need the steps..
Thanks

[2x / (x + 3)] – [x / (x – 3)] = (5x + 2) / (x + 3), x ≠ ±3

Multiply both sides by the lowest common denominator, (x – 3)(x + 3), to eliminate the fractions.

2x(x – 3) – x(x + 3) = (5x + 2)(x – 3)
2x² – 6x – x² – 3x = 5x² – 13x – 6
x² – 9x = 5x² – 13x – 6
4x² – 4x – 6 = 0
2x² – 2x – 3 = 0

Now, use the quadratic formula, x = [ -b ± √(b² – 4ac) ] / (2a), with a = 2, b = -2, and c = -3.

x = (2 ± √28) / 4
x = (2 ± √4√7) / 4
x = (2 ± 2√7) / 4
x = (1 ± √7) / 2

Thus, the solution is x = (1 ± √7) / 2.