Use the quadratic formula to solve 5x + 6x^2 + 3 = 0. What are the values of x?

The quadratic formula is:

x = (-b ± sqrt(b^2 – 4ac)) / (2a)

where a, b, and c are coefficients of the quadratic equation ax^2 + bx + c = 0.

In the given equation, we have:

a = 6 b = 5 c = 3

Substituting these values into the quadratic formula, we get:

x = (-5 ± sqrt(5^2 – 4(6)(3))) / (2(6)) x = (-5 ± sqrt(25 – 72)) / 12 x = (-5 ± sqrt(-47)) / 12

Since the square root of a negative number is not a real number, this equation has no real solutions.

Therefore, the values of x are complex numbers:

x = (-5 + i√47) / 12 or x = (-5 – i√47) / 12, where i is the imaginary unit.