Solve Using the Quadratic Formula 10x^2-7x+5=0

$10 x^{2} - 7 x + 5 = 0$

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 $a = 10$ , $b = - 7$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (10 \cdot 5)}}{2 \cdot 10}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 10 \cdot 5}}{2 \cdot 10}$

Multiply $- 4 \cdot 10 \cdot 5$ .

Multiply $- 4$ by $10$ .

$x = \frac{7 \pm \sqrt{49 - 40 \cdot 5}}{2 \cdot 10}$

Multiply $- 40$ by $5$ .

$x = \frac{7 \pm \sqrt{49 - 200}}{2 \cdot 10}$

Subtract $200$ from $49$ .

$x = \frac{7 \pm \sqrt{- 151}}{2 \cdot 10}$

Rewrite $- 151$ as $- 1 (151)$ .

$x = \frac{7 \pm \sqrt{- 1 \cdot 151}}{2 \cdot 10}$

Rewrite $\sqrt{- 1 (151)}$ as $\sqrt{- 1} \cdot \sqrt{151}$ .

$x = \frac{7 \pm \sqrt{- 1} \cdot \sqrt{151}}{2 \cdot 10}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{7 \pm i \sqrt{151}}{2 \cdot 10}$

Multiply $2$ by $10$ .

$x = \frac{7 \pm i \sqrt{151}}{20}$