Solve Using the Quadratic Formula 10x^2-16x+6=0

$10 x^{2} - 16 x + 6 = 0$

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 $a = 10$ , $b = - 16$ , and $c = 6$ into the quadratic formula and solve for $x$ .

$\frac{16 \pm \sqrt{{(- 16)}^{2} - 4 \cdot (10 \cdot 6)}}{2 \cdot 10}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 10 \cdot 6}}{2 \cdot 10}$

Multiply $- 4 \cdot 10 \cdot 6$ .

Multiply $- 4$ by $10$ .

$x = \frac{16 \pm \sqrt{256 - 40 \cdot 6}}{2 \cdot 10}$

Multiply $- 40$ by $6$ .

$x = \frac{16 \pm \sqrt{256 - 240}}{2 \cdot 10}$

Subtract $240$ from $256$ .

$x = \frac{16 \pm \sqrt{16}}{2 \cdot 10}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{16 \pm \sqrt{4^{2}}}{2 \cdot 10}$

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

$x = \frac{16 \pm 4}{2 \cdot 10}$

Multiply $2$ by $10$ .

$x = \frac{16 \pm 4}{20}$

Simplify $\frac{16 \pm 4}{20}$ .

$x = \frac{4 \pm 1}{5}$

Step 4

The final answer is the combination of both solutions.

$x = 1, \frac{3}{5}$