Solve the Quadratic: Finding x in 4x² = 12x - 9

To solve the quadratic equation $4x^2 = 12x - 9$, we begin by rewriting it in standard quadratic form:

$4x^2 - 12x + 9 = 0$

Here, we compare to the general form $ax^2 + bx + c = 0$ and identify:

• $a = 4$
• $b = -12$
• $c = 9$

We will now use the quadratic formula:

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

Substitute in the values for $a$, $b$, and $c$:

$x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4 \cdot 4 \cdot 9}}{2 \cdot 4}$

Simplify:

$x = \frac{12 \pm \sqrt{144 - 144}}{8}$

$x = \frac{12 \pm \sqrt{0}}{8}$

$x = \frac{12 \pm 0}{8}$

This simplifies further to:

$x = \frac{12}{8} = \frac{3}{2}$

Therefore, the solution to the equation $4x^2 = 12x - 9$ is $x = \frac{3}{2}$.