(x/(2-x))^2=6/15 without quadratic formula

(x/(2-x))^2=6/15   simplifying, we have

x^2 / ( x^2 - 4x + 4)  = 6 / 15      cross- multiply

15x^2  = 6(x^2 - 4x + 4)     divide both sides by 3

5x^2 = 2(x^2 - 4x + 4)

5x^2 = 2x^2 - 8x + 8

3x^2 + 8x - 8 = 0          divide both sides by 3

x^2 + (8/3)x - 8/3  = 0    complete the square

x^2 + (8/3)x + 16/9  = 8/3 + 16/9

(x + 4/3) ^2  = 24/9 + 16/9

(x + 4/3) ^2  = 40/9     take both roots

x + 4/3   = ±(2/3)√10

x = [ - 4 ± 2√10 ] / 3