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

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

Step 1

Subtract $4$ from both sides of the equation.

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

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

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

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

Step 4

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $5$ .

$x = \frac{- 9 \pm \sqrt{81 - 20 \cdot - 4}}{2 \cdot 5}$

Multiply $- 20$ by $- 4$ .

$x = \frac{- 9 \pm \sqrt{81 + 80}}{2 \cdot 5}$

Add $81$ and $80$ .

$x = \frac{- 9 \pm \sqrt{161}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 9 \pm \sqrt{161}}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 9 \pm \sqrt{161}}{10}$

Decimal Form:

$x = 0.36885775 \dots, - 2.16885775 \dots$