To solve the quadratic equation 4x^2 – 5x – 12 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± sqrt(b^2 – 4ac)) / (2a)

Comparing the given equation 4x^2 – 5x – 12 = 0 to the standard form ax^2 + bx + c = 0, we have a = 4, b = -5, and c = -12. Substituting these values into the quadratic formula, we can calculate the solutions for x.

x = (-(-5) ± sqrt((-5)^2 – 4 * 4 * (-12))) / (2 * 4) x = (5 ± sqrt(25 + 192)) / 8 x = (5 ± sqrt(217)) / 8

Therefore, the solutions for the given quadratic equation are:

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