Solve Using the Quadratic Formula 3x^2-11x+4=0

$3 x^{2} - 11 x + 4 = 0$

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 $a = 3$ , $b = - 11$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (3 \cdot 4)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 3 \cdot 4}}{2 \cdot 3}$

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

Multiply $- 4$ by $3$ .

$x = \frac{11 \pm \sqrt{121 - 12 \cdot 4}}{2 \cdot 3}$

Multiply $- 12$ by $4$ .

$x = \frac{11 \pm \sqrt{121 - 48}}{2 \cdot 3}$

Subtract $48$ from $121$ .

$x = \frac{11 \pm \sqrt{73}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{11 \pm \sqrt{73}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11 \pm \sqrt{73}}{6}$

Decimal Form:

$x = 3.25733395 \dots, 0.40933270 \dots$