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

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

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 $a = 4$ , $b = 1$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (4 \cdot - 9)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

One to any power is one.

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

Multiply $- 4 \cdot 4 \cdot - 9$ .

Multiply $- 4$ by $4$ .

$x = \frac{- 1 \pm \sqrt{1 - 16 \cdot - 9}}{2 \cdot 4}$

Multiply $- 16$ by $- 9$ .

$x = \frac{- 1 \pm \sqrt{1 + 144}}{2 \cdot 4}$

Add $1$ and $144$ .

$x = \frac{- 1 \pm \sqrt{145}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 1 \pm \sqrt{145}}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1 \pm \sqrt{145}}{8}$

Decimal Form:

$x = 1.38019932 \dots, - 1.63019932 \dots$