Solve Using the Quadratic Formula 4x^2+9x+5=0

$4 x^{2} + 9 x + 5 = 0$

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 $a = 4$ , $b = 9$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (4 \cdot 5)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raise $9$ to the power of $2$ .

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 4 \cdot 5}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{- 9 \pm \sqrt{81 - 16 \cdot 5}}{2 \cdot 4}$

Multiply $- 16$ by $5$ .

$x = \frac{- 9 \pm \sqrt{81 - 80}}{2 \cdot 4}$

Subtract $80$ from $81$ .

$x = \frac{- 9 \pm \sqrt{1}}{2 \cdot 4}$

Any root of $1$ is $1$ .

$x = \frac{- 9 \pm 1}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 9 \pm 1}{8}$

Step 4

The final answer is the combination of both solutions.

$x = - 1, - \frac{5}{4}$