Solve Using the Quadratic Formula 9x^2-7x=3

$9 x^{2} - 7 x = 3$

Step 1

Subtract $3$ from both sides of the equation.

$9 x^{2} - 7 x - 3 = 0$

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 $a = 9$ , $b = - 7$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (9 \cdot - 3)}}{2 \cdot 9}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 9 \cdot - 3}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 3$ .

Multiply $- 4$ by $9$ .

$x = \frac{7 \pm \sqrt{49 - 36 \cdot - 3}}{2 \cdot 9}$

Multiply $- 36$ by $- 3$ .

$x = \frac{7 \pm \sqrt{49 + 108}}{2 \cdot 9}$

Add $49$ and $108$ .

$x = \frac{7 \pm \sqrt{157}}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{7 \pm \sqrt{157}}{18}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \pm \sqrt{157}}{18}$

Decimal Form:

$x = 1.08499800 \dots, - 0.30722022 \dots$