(2x+7)(2x-7) + 30 = 6x(1-x)

Expanding the left side:

4x^2 - 49 + 30 = 6x - 6x^2
4x^2 - 19 = 6x - 6x^2

Rearranging the equation:

10x^2 - 6x - 19 = 0

Now we have a quadratic equation that can be solved using the quadratic formula:

x = (-(-6) ± √((-6)^2 - 4(10)(-19))) / 2(10)
x = (6 ± √(36 + 760)) / 20
x = (6 ± √796) / 20
x = (6 ± 28.2) / 20

Therefore, the solutions are:
x₁ = (6 + 28.2) / 20 = 34.2 / 20 = 1.71
x₂ = (6 - 28.2) / 20 = -22.2 / 20 = -1.11

So the solutions are x = 1.71 and x = -1.11.