To solve the quadratic equation 4x^2 + 3x - 10 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = 4, b = 3, and c = -10. Substituting these values into the formula, we get:

x = (-3 ± √(3^2 - 44-10)) / 2*4
x = (-3 ± √(9 + 160)) / 8
x = (-3 ± √169) / 8
x = (-3 ± 13) / 8

Therefore, the solutions to the quadratic equation 4x^2 + 3x - 10 = 0 are:
x1 = (-3 + 13) / 8 = 10 / 8 = 1.25
x2 = (-3 - 13) / 8 = -16 / 8 = -2

So the solutions are x = 1.25 and x = -2.