Final answer:
To solve the equation x(x+1)-56=4x(x-7), expand both sides and combine like terms. Factor the resulting quadratic equation or use the quadratic formula to find the solutions. The solutions are x = 4 and x = 14/3.
Step-by-step explanation:
To solve the equation x(x+1)-56=4x(x-7), we can start by expanding both sides of the equation:
x^2 + x - 56 = 4x^2 - 28x
Combining like terms, we get:
3x^2 - 29x + 56 = 0
Next, we can factor the quadratic equation or use the quadratic formula to find the solutions. Factoring the equation, we get:
(x-4)(3x-14) = 0
Setting each factor equal to zero, we find two solutions:
x - 4 = 0 --> x = 4
3x - 14 = 0 --> x = 14/3
Therefore, there are two solutions to the given equation: x = 4 and x = 14/3.