Question

What are the roots of -12x2 + 11x − 3 = 0?

Answer 1

This quadratic does not have any real roots.
It is a parabola that opens downward with vertex at (11/24, -.48) which means the vertex is below the x-axis and therefore will not have any real roots.

Imaginary roots would be
x = [11 +- sqrt (121 - 4(-12)(-3)] / (-24)
x = [11 + - i sqrt(23) ] / (-24)