Solve the Quadratic Equation: 3x² - 39x - 90 = 0

To solve the quadratic equation $3x^2 - 39x - 90 = 0$, we will use the quadratic formula.

• Step 1: Identify coefficients: $a = 3$, $b = -39$, and $c = -90$.
• Step 2: Calculate the discriminant: $b^2 - 4ac$.
• Step 3: Apply the quadratic formula to find $x_1$ and $x_2$.

Now, let's work through the steps:

Step 1: Coefficients are given as $a = 3$, $b = -39$, $c = -90$.

Step 2: The discriminant is calculated as follows:

$b^2 - 4ac = (-39)^2 - 4 \cdot 3 \cdot (-90) = 1521 + 1080 = 2601$.

The discriminant is positive, indicating two distinct real solutions.

Step 3: Apply the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-(-39) \pm \sqrt{2601}}{2 \cdot 3}$

This simplifies to:

$x = \frac{39 \pm 51}{6}$

Calculating the two solutions:

• $x_1 = \frac{39 + 51}{6} = \frac{90}{6} = 15$.
• $x_2 = \frac{39 - 51}{6} = \frac{-12}{6} = -2$.

Therefore, the solutions to the equation are $x_1 = 15$ and $x_2 = -2$.

Comparing with the choices, the correct answer is:

$x_1 = 15$ $x_2 = -2$