Solve Using the Quadratic Formula -5x^2+7x=-9

$- 5 x^{2} + 7 x = - 9$

Step 1

Add $9$ to both sides of the equation.

$- 5 x^{2} + 7 x + 9 = 0$

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 $a = - 5$ , $b = 7$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (- 5 \cdot 9)}}{2 \cdot - 5}$

Step 4

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot - 5 \cdot 9}}{2 \cdot - 5}$

Multiply $- 4 \cdot - 5 \cdot 9$ .

Multiply $- 4$ by $- 5$ .

$x = \frac{- 7 \pm \sqrt{49 + 20 \cdot 9}}{2 \cdot - 5}$

Multiply $20$ by $9$ .

$x = \frac{- 7 \pm \sqrt{49 + 180}}{2 \cdot - 5}$

Add $49$ and $180$ .

$x = \frac{- 7 \pm \sqrt{229}}{2 \cdot - 5}$

Multiply $2$ by $- 5$ .

$x = \frac{- 7 \pm \sqrt{229}}{- 10}$

Simplify $\frac{- 7 \pm \sqrt{229}}{- 10}$ .

$x = \frac{7 \pm \sqrt{229}}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \pm \sqrt{229}}{10}$

Decimal Form:

$x = 2.21327459 \dots, - 0.81327459 \dots$