For what value of g does the function fg g^2 + 3g equal 18?

To solve the equation g² + 3g = 18, we start by rearranging the equation:

g² + 3g – 18 = 0

This is a standard quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 3, and c = -18.

Next, we can use the quadratic formula to find the values of g:

g = (-b ± √(b² – 4ac)) / (2a)

Plugging in the values, we calculate:

g = (−3 ± √(3² – 4 * 1 * (-18))) / (2 * 1)

This simplifies to:

g = (−3 ± √(9 + 72)) / 2

g = (−3 ± √81) / 2

g = (−3 ± 9) / 2

This gives us two possible solutions:

g = (6) / 2 = 3

or

g = (−12) / 2 = −6

Thus, the values of g that satisfy the equation g² + 3g = 18 are g = 3 and g = −6.