Solve the Quadratic Equation: 4x² - 6x - 4 = 0 Step-by-Step

To solve the quadratic equation $4x^2 - 6x - 4 = 0$, we will apply the quadratic formula.

Given the quadratic equation is of the form $ax^2 + bx + c = 0$, we identify:

• $a = 4$
• $b = -6$
• $c = -4$

Next, we use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Calculate the discriminant:

$b^2 - 4ac = (-6)^2 - 4 \times 4 \times (-4)$

$b^2 - 4ac = 36 + 64 = 100$

Since the discriminant is positive, we have two real solutions.

Now, plug the values into the quadratic formula:

$x = \frac{-(-6) \pm \sqrt{100}}{2 \times 4}$

$x = \frac{6 \pm 10}{8}$

Solving for the two values of $x$:

• First solution: $x_1 = \frac{6 + 10}{8} = \frac{16}{8} = 2$
• Second solution: $x_2 = \frac{6 - 10}{8} = \frac{-4}{8} = -\frac{1}{2}$

Therefore, the solutions to the equation are $x_1 = 2$ and $x_2 = -\frac{1}{2}$.