i'm a bit stuck with this..

145/18 = x + x^2

what does x equal to?

multiply each term by 18, then re-arrange to get
18x^2 + 18x - 145 = 0

This quadratic does not factor, so use the quadratic formula to get your two answers.

To solve the quadratic equation 18x^2 + 18x - 145 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 18, b = 18, and c = -145. Substituting these values into the quadratic formula, we get:

x = (-(18) ± √((18)^2 - 4(18)(-145))) / (2(18))

Simplifying further:

x = (-18 ± √(324 + 10440)) / 36
x = (-18 ± √10764) / 36
x = (-18 ± 103.758) / 36

So the two possible values for x are:

x1 = (-18 + 103.758) / 36 ≈ 2.516
x2 = (-18 - 103.758) / 36 ≈ -3.648

Therefore, the equation 145/18 = x + x^2 has two possible solutions: x ≈ 2.516 and x ≈ -3.648.