Subtracting 2x^2 + 9x - 8 from both sides, we get:
x^2 + 2x - 4 = -8
Rearranging terms and simplifying:
x^2 + 2x - 4 + 8 = 0 x^2 + 2x + 4 = 0
The equation x^2 + 2x + 4 = 0 does not have real roots since the discriminant (b^2 - 4ac) is less than zero. Thus, the original equation (3x-1)(x+4) = (2x+3)(x+3) - 17 does not have a solution in real numbers.
Expanding both sides of the equation, we have:
(3x-1)(x+4) = (2x+3)(x+3) - 17
3x^2 + 12x - x - 4 = 2x^2 + 6x + 3x + 9 - 17
3x^2 + 11x - 4 = 2x^2 + 9x - 8
3x^2 + 11x - 4 = 2x^2 + 9x - 8
Subtracting 2x^2 + 9x - 8 from both sides, we get:
x^2 + 2x - 4 = -8
Rearranging terms and simplifying:
x^2 + 2x - 4 + 8 = 0
x^2 + 2x + 4 = 0
The equation x^2 + 2x + 4 = 0 does not have real roots since the discriminant (b^2 - 4ac) is less than zero. Thus, the original equation (3x-1)(x+4) = (2x+3)(x+3) - 17 does not have a solution in real numbers.