### Solve: 4x ^ 2 – 5x – 12 = 0

To solve the equation 4x^2 – 5x – 12 = 0, we can use the quadratic formula, which gives:

x = (-b ± sqrt(b^2 – 4ac)) / 2a

Here, a = 4, b = -5, and c = -12, so substituting these values, we get:

x = (-(-5) ± sqrt((-5)^2 – 4(4)(-12))) / 2(4)

Simplifying the expression under the square root, we get:

x = (5 ± sqrt(25 + 192)) / 8

x = (5 ± sqrt(217)) / 8

Therefore, the solutions to the equation 4x^2 – 5x – 12 = 0 are:

x = (5 + sqrt(217)) / 8

x = (5 – sqrt(217)) / 8

So, x can be approximated to:

x ≈ 2.25 or x ≈ -1.75

Hence, the solutions to the equation are x ≈ 2.25 and x ≈ -1.75.

### Solve: x + 9 = 18 + -2x

To solve the equation x + 9 = 18 – 2x, we can first simplify it by adding 2x to both sides, which gives:

x + 2x + 9 = 18

Combining like terms, we get:

3x + 9 = 18

Next, we can isolate x on one side by subtracting 9 from both sides, which gives:

3x = 9

Finally, we can solve for x by dividing both sides by 3, which gives:

x = 3

Therefore, the solution to the equation x + 9 = 18 – 2x is x = 3.