Solve Using the Quadratic Formula 3x^2+11x+5=0

$3 x^{2} + 11 x + 5 = 0$

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 $a = 3$ , $b = 11$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{- 11 \pm \sqrt{11^{2} - 4 \cdot (3 \cdot 5)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot 3 \cdot 5}}{2 \cdot 3}$

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

Multiply $- 4$ by $3$ .

$x = \frac{- 11 \pm \sqrt{121 - 12 \cdot 5}}{2 \cdot 3}$

Multiply $- 12$ by $5$ .

$x = \frac{- 11 \pm \sqrt{121 - 60}}{2 \cdot 3}$

Subtract $60$ from $121$ .

$x = \frac{- 11 \pm \sqrt{61}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 11 \pm \sqrt{61}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 11 \pm \sqrt{61}}{6}$

Decimal Form:

$x = - 0.53162505 \dots, - 3.13504161 \dots$