17x + 2x^2 + 21 = 0

The equation is a quadratic equation of the form ax^2 + bx + c = 0.

Rearranging the terms, we get 2x^2 + 17x + 21 = 0.

Using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / 2a, where a=2, b=17, c=21.

x = [-17 ± sqrt(17^2 - 4*2*21)] / (2*2)

x = [-17 ± sqrt(289 - 168)] / 4

x = [-17 ± sqrt(121)] / 4

x = [-17 ± 11] / 4

The two solutions are x1 = (-17 + 11) / 4 = -6 / 4 = -3/2 and x2 = (-17 - 11) / 4 = -28 / 4 = -7.