The problem asks us to find the values of $x$ that satisfy the equation $5x = 3x^2 - 9x + 12$. We need to give the solutions to 3 significant figures.

1. Problem Description

The problem asks us to find the values of $x$ that satisfy the equation $5x = 3x^2 - 9x + 12$. We need to give the solutions to 3 significant figures.

2. Solution Steps

First, we rewrite the equation in the standard quadratic form $ax^2 + bx + c = 0$:

$3x^2 - 9x + 12 - 5x = 0$

$3x^2 - 14x + 12 = 0$

Now, we can use the quadratic formula to solve for $x$:

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

In this case, $a = 3$, $b = -14$, and $c = 12$. Substituting these values into the quadratic formula:

$x = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(3)(12)}}{2(3)}$

$x = \frac{14 \pm \sqrt{196 - 144}}{6}$

$x = \frac{14 \pm \sqrt{52}}{6}$

$x = \frac{14 \pm 2\sqrt{13}}{6}$

$x = \frac{7 \pm \sqrt{13}}{3}$

So, the two possible values for $x$ are:

$x_1 = \frac{7 + \sqrt{13}}{3}$ and $x_2 = \frac{7 - \sqrt{13}}{3}$.

Now, we approximate these values to 3 significant figures:

$x_1 = \frac{7 + \sqrt{13}}{3} \approx \frac{7 + 3.60555}{3} \approx \frac{10.60555}{3} \approx 3.53518 \approx 3.54$

$x_2 = \frac{7 - \sqrt{13}}{3} \approx \frac{7 - 3.60555}{3} \approx \frac{3.39445}{3} \approx 1.13148 \approx 1.13$

3. Final Answer

The values of $x$ to 3 significant figures are $x = 3.54$ and $x = 1.13$.