Solve Using the Quadratic Formula 9x^2+3x=20

$9 x^{2} + 3 x = 20$

Step 1

Subtract $20$ from both sides of the equation.

$9 x^{2} + 3 x - 20 = 0$

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 $a = 9$ , $b = 3$ , and $c = - 20$ into the quadratic formula and solve for $x$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (9 \cdot - 20)}}{2 \cdot 9}$

Step 4

Simplify.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot 9 \cdot - 20}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 20$ .

Multiply $- 4$ by $9$ .

$x = \frac{- 3 \pm \sqrt{9 - 36 \cdot - 20}}{2 \cdot 9}$

Multiply $- 36$ by $- 20$ .

$x = \frac{- 3 \pm \sqrt{9 + 720}}{2 \cdot 9}$

Add $9$ and $720$ .

$x = \frac{- 3 \pm \sqrt{729}}{2 \cdot 9}$

Rewrite $729$ as $27^{2}$ .

$x = \frac{- 3 \pm \sqrt{27^{2}}}{2 \cdot 9}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 3 \pm 27}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{- 3 \pm 27}{18}$

Simplify $\frac{- 3 \pm 27}{18}$ .

$x = \frac{- 1 \pm 9}{6}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{4}{3}, - \frac{5}{3}$