To solve the quadratic equation 2x^2 + 11x - 21 = 0, we can use the quadratic formula.

The quadratic formula is given by: x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 2, b = 11, and c = -21.

Plugging these values into the formula, we get:

x = (-11 ± sqrt(11^2 - 4(2)(-21))) / 2(2)
x = (-11 ± sqrt(121 + 168)) / 4
x = (-11 ± sqrt(289)) / 4
x = (-11 ± 17) / 4

Therefore, we have two possible solutions:

x1 = (-11 + 17) / 4 = 6 / 4 = 1.5
x2 = (-11 - 17) / 4 = -28 / 4 = -7

So, the solutions to the equation 2x^2 + 11x - 21 = 0 are x = 1.5 and x = -7.