Find the exact solutions to the quadratic equation below, using the quadratic formula. Enter the smaller number first.−3x2−5x+2=0

The quadratic formula is given by:

x = [-b ± sqrt(b² - 4ac)] / 2a

In the equation -3x² - 5x + 2 = 0, the coefficients are a = -3, b = -5, and c = 2.

First, calculate the discriminant, which is b² - 4ac:

Discriminant = (-5)² - 4*(-3)*2 = 25 + 24 = 49

Since the discriminant is positive, there are two distinct real roots.

Now, substitute a, b, and the discriminant into the quadratic formula to find the solutions:

x = [5 ± sqrt(49)] / 2*(-3) x = [5 ± 7] / -6

So the solutions are x = -2/3 and x = -4.

The smaller number is -4.