Solve Using the Quadratic Formula 5x^2-8x+3=0

$5 x^{2} - 8 x + 3 = 0$

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 $a = 5$ , $b = - 8$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (5 \cdot 3)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 5 \cdot 3}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 3$ .

Multiply $- 4$ by $5$ .

$x = \frac{8 \pm \sqrt{64 - 20 \cdot 3}}{2 \cdot 5}$

Multiply $- 20$ by $3$ .

$x = \frac{8 \pm \sqrt{64 - 60}}{2 \cdot 5}$

Subtract $60$ from $64$ .

$x = \frac{8 \pm \sqrt{4}}{2 \cdot 5}$

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

$x = \frac{8 \pm \sqrt{2^{2}}}{2 \cdot 5}$

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

$x = \frac{8 \pm 2}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{8 \pm 2}{10}$

Simplify $\frac{8 \pm 2}{10}$ .

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

Step 4

The final answer is the combination of both solutions.

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