To solve the equation X² - 7x = 3 + x, we first need to move all the terms to one side of the equation to set it equal to zero.

X² - 7x - 3 - x = 0
X² - 8x - 3 = 0

Now we have a quadratic equation in the form of Ax² + Bx + C = 0.

To solve this quadratic equation, we can use the quadratic formula: x = (-B ± √(B² - 4AC))/2A

In this case, A = 1, B = -8, C = -3.

Plugging in the values, we get:
x = (8 ± √((-8)² - 4(1)(-3)))/2(1)
x = (8 ± √(64 + 12))/2
x = (8 ± √76)/2
x = (8 ± √(4*19))/2
x = (8 ± 2√19)/2
x = 4 ± √19

Therefore, the solutions to the equation X² - 7x = 3 + x are x = 4 + √19 and x = 4 - √19.