Solve the Quadratic Equation: 81x² - 216 + 144 = 0

To solve the quadratic equation $81x^2 - 216x + 144 = 0$, we begin by identifying the coefficients: $a = 81$, $b = -216$, and $c = 144$.

Next, we use the quadratic formula:

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

Substitute the values of $a$, $b$, and $c$ into the formula:

$b^2 - 4ac = (-216)^2 - 4 \cdot 81 \cdot 144$

$= 46656 - 46656 = 0$

The discriminant is zero, indicating there is exactly one real solution. Substitute back into the quadratic formula:

$x = \frac{-(-216) \pm \sqrt{0}}{2 \cdot 81}$

$x = \frac{216 \pm 0}{162}$

$x = \frac{216}{162}$

Simplify the fraction:

$x = \frac{216 \div 54}{162 \div 54} = \frac{4}{3}$

Therefore, the solution to the equation is $x = \frac{4}{3}$.

By comparing with the given choices, choice 1: $x = \frac{4}{3}$ is correct.