Solve Using the Quadratic Formula 2x^2-13x+21=0

$2 x^{2} - 13 x + 21 = 0$

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 $a = 2$ , $b = - 13$ , and $c = 21$ into the quadratic formula and solve for $x$ .

$\frac{13 \pm \sqrt{{(- 13)}^{2} - 4 \cdot (2 \cdot 21)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 13$ to the power of $2$ .

$x = \frac{13 \pm \sqrt{169 - 4 \cdot 2 \cdot 21}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 21$ .

Multiply $- 4$ by $2$ .

$x = \frac{13 \pm \sqrt{169 - 8 \cdot 21}}{2 \cdot 2}$

Multiply $- 8$ by $21$ .

$x = \frac{13 \pm \sqrt{169 - 168}}{2 \cdot 2}$

Subtract $168$ from $169$ .

$x = \frac{13 \pm \sqrt{1}}{2 \cdot 2}$

Any root of $1$ is $1$ .

$x = \frac{13 \pm 1}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{13 \pm 1}{4}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{7}{2}, 3$