Solve 9x^2 + 12x - 24 = 0

x = (-2 + √3) / 3 and (-2 - √3) / 3

Step-by-step explanation:

Use quadratic equation to solve.

The standard form of a quadratic equation is

y = ax² + bx + c

For our equation, we have a = 9, b = 12, and c = - 24

Quadratic equation is ...

x = - b / (2a) ± [√ (b² - 4ac) / (2a) ]

Plug in our values and simplify ...

x = - 12 / (2*9) ± [√ (12² - 4 (9) (-24)) / (2*9) ]

x = - 12/18 ± [√ (144 + 864) / 18]

x = - 2/3 ± (√1008) / 18

√1008 = 12√7 (use a factor tree)

So x = - 2/3 ± (12√7) / 18

x = - 2/3 ± (√7) / 3

x = (-2 ± √7) / 3

x = (-2 + √3) / 3 and (-2 - √3) / 3