Use the discriminant, $LaTeX: \displaystyle b^2-4ac$ to determine the number and type of solutions to the equation $LaTeX: \displaystyle 4 x^{2} + 7 x + 2 = 0$ . No points will be given if the discriminant is not used.

Since the discriminant is $LaTeX: \displaystyle b^2-4ac=(7)^2-4(4)(2)=17$ and is positive, the equation has two real solutions.