Use the discriminant, $LaTeX: \displaystyle b^2-4ac$ to determine the number and type of solutions to the equation $LaTeX: \displaystyle - 5 x^{2} - 8 x + 3 = 0$ . No points will be given if the discriminant is not used.

Since the discriminant is $LaTeX: \displaystyle b^2-4ac=(-8)^2-4(-5)(3)=124$ and is positive, the equation has two real solutions.