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

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

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 $a = 3$ , $b = - 5$ , and $c = 2$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

Raise $- 5$ to the power of $2$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 3 \cdot 2}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 2$ .

Multiply $- 4$ by $3$ .

$x = \frac{5 \pm \sqrt{25 - 12 \cdot 2}}{2 \cdot 3}$

Multiply $- 12$ by $2$ .

$x = \frac{5 \pm \sqrt{25 - 24}}{2 \cdot 3}$

Subtract $24$ from $25$ .

$x = \frac{5 \pm \sqrt{1}}{2 \cdot 3}$

Any root of $1$ is $1$ .

$x = \frac{5 \pm 1}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{5 \pm 1}{6}$

Step 4

The final answer is the combination of both solutions.

$x = 1, \frac{2}{3}$