The quadratic formula is used to solve for the roots of the equation:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values of a=1, b=2, and c=-8 into the formula:

x = (-2 ± √(2^2 - 41(-8))) / 2*1
x = (-2 ± √(4 + 32)) / 2
x = (-2 ± √36) / 2
x = (-2 ± 6) / 2

Therefore, the roots of the equation are:

x1 = (-2 + 6) / 2 = 4 / 2 = 2
x2 = (-2 - 6) / 2 = -8 / 2 = -4

So, the solutions to the equation 1x^2 + 2x - 8 = 0 are x = 2 and x = -4.