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

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Expanding the left side:

(2x+7)(2x-7) + 30

= 4x^2 - 14x + 14x - 49 + 30
= 4x^2 - 19

Expanding the right side:

6x(1-x)

= 6x - 6x^2

Setting both sides equal to each other:

4x^2 - 19 = 6x - 6x^2

Rearranging the equation:

4x^2 + 6x^2 - 6x - 19 - 6x = 0
10x^2 - 12x - 19 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-(-12) ± √((-12)^2 - 410(-19))) / 2*10
x = (12 ± √(144 + 760)) / 20
x = (12 ± √904) / 20
x = (12 ± 30.066) / 20

Therefore, the solutions for x are:

x = (12 + 30.066) / 20 = 42.066 / 20 = 2.10

or

x = (12 - 30.066) / 20 = -18.066 / 20 = -0.90

So the solutions for the equation are x = 2.10 and x = -0.90.