(5x+6)^2/3=(9+4x)^2/3

Solution for (5x+6)^2/3=(9+4x)^2/3 equation:

x in (-oo:+oo)

((5*x+6)^2)/3 = ((4*x+9)^2)/3 // - ((4*x+9)^2)/3

((5*x+6)^2)/3-(((4*x+9)^2)/3) = 0

((5*x+6)^2)/3+(-1*(4*x+9)^2)/3 = 0

(5*x+6)^2-1*(4*x+9)^2 = 0

9*x^2-12*x-45 = 0

9*x^2-12*x-45 = 0

3*(3*x^2-4*x-15) = 0

3*x^2-4*x-15 = 0

DELTA = (-4)^2-(-15*3*4)

DELTA = 196

DELTA > 0

x = (196^(1/2)+4)/(2*3) or x = (4-196^(1/2))/(2*3)

x = 3 or x = -5/3

3*(x+5/3)*(x-3) = 0

(3*(x+5/3)*(x-3))/3 = 0

(3*(x+5/3)*(x-3))/3 = 0 // * 3

3*(x+5/3)*(x-3) = 0

( x+5/3 )

x+5/3 = 0 // - 5/3

x = -5/3

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -5/3, 3 }