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

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

Step 1

Subtract $9 x$ from both sides of the equation.

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

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 $a = 1$ , $b = - 9$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (1 \cdot 3)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 1 \cdot 3}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 3$ .

Multiply $- 4$ by $1$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 3}}{2 \cdot 1}$

Multiply $- 4$ by $3$ .

$x = \frac{9 \pm \sqrt{81 - 12}}{2 \cdot 1}$

Subtract $12$ from $81$ .

$x = \frac{9 \pm \sqrt{69}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{9 \pm \sqrt{69}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9 \pm \sqrt{69}}{2}$

Decimal Form:

$x = 8.65331193 \dots, 0.34668806 \dots$