Question

for the few questions in this set, you will see the quadratic formula. soon, you will need to answer the questions without this reminder.
$x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }$ for $ax^2 + bx + c = 0$
solve for x. write both solutions, separated by a comma.
$3x^2 + 4x - 15 = 0$
enter the correct answer.

Explanation:

Step1: Identify a, b, c

From $3x^2 + 4x - 15 = 0$, we get $a=3$, $b=4$, $c=-15$.

Step2: Calculate discriminant

$\Delta = b^2 - 4ac = 4^2 - 4(3)(-15) = 16 + 180 = 196$

Step3: Substitute into quadratic formula

$x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{-4 \pm \sqrt{196}}{2(3)} = \frac{-4 \pm 14}{6}$

Step4: Solve for both roots

First root: $x = \frac{-4 + 14}{6} = \frac{10}{6} = \frac{5}{3}$
Second root: $x = \frac{-4 - 14}{6} = \frac{-18}{6} = -3$

Answer:

$\frac{5}{3}, -3$