To find the solutions for x, we can use various methods, such as factoring, completing the square, or applying the quadratic formula. Let’s solve it using the quadratic formula, which is a widely applicable method.

The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 – 4ac)) / (2a)

By comparing the given equation to the standard form, we can determine the values of a, b, and c:

a = 4 b = -5 c = -12

Substituting these values into the quadratic formula, we can calculate the solutions for x:

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

Hence, the solutions for the given quadratic equation are: x = (5 + √217) / 8 x = (5 – √217) / 8

Please note that these solutions are approximate values, as √217 is an irrational number.