4x ^ 2 – 5x – 12 = 0

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

x = (-b Â± sqrt(b^2 – 4ac)) / 2a

where a, b, and c are coefficients of the equation in the form ax^2 + bx + c.

Substituting the values from the given equation, we get:

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

Simplifying this expression, we get:

x = (5 Â± sqrt(25 + 192)) / 8

x = (5 Â± sqrt(217)) / 8

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

x = (5 + sqrt(217)) / 8 â‰ˆ 2.346

x = (5 – sqrt(217)) / 8 â‰ˆ -1.281

So, the values of x that satisfy the equation are approximately 2.346 and -1.281.