Solve Using the Quadratic Formula 3x^2-16x+16=0

$3 x^{2} - 16 x + 16 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 3$ , $b = - 16$ , and $c = 16$ into the quadratic formula and solve for $x$ .

$\frac{16 \pm \sqrt{{(- 16)}^{2} - 4 \cdot (3 \cdot 16)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 16$ to the power of $2$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 3 \cdot 16}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 16$ .

Multiply $- 4$ by $3$ .

$x = \frac{16 \pm \sqrt{256 - 12 \cdot 16}}{2 \cdot 3}$

Multiply $- 12$ by $16$ .

$x = \frac{16 \pm \sqrt{256 - 192}}{2 \cdot 3}$

Subtract $192$ from $256$ .

$x = \frac{16 \pm \sqrt{64}}{2 \cdot 3}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{16 \pm \sqrt{8^{2}}}{2 \cdot 3}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{16 \pm 8}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{16 \pm 8}{6}$

Simplify $\frac{16 \pm 8}{6}$ .

$x = \frac{8 \pm 4}{3}$

Step 4

The final answer is the combination of both solutions.

$x = 4, \frac{4}{3}$