Find the Roots (Zeros) x^2+30=-9x

$x^{2} + 30 = - 9 x$

Add $9 x$ to both sides of the equation.

$x^{2} + 30 + 9 x = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = 9$ , and $c = 30$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (1 \cdot 30)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

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

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 1 \cdot 30}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 30}}{2 \cdot 1}$

Multiply $- 4$ by $30$ .

$x = \frac{- 9 \pm \sqrt{81 - 120}}{2 \cdot 1}$

Subtract $120$ from $81$ .

$x = \frac{- 9 \pm \sqrt{- 39}}{2 \cdot 1}$

Rewrite $- 39$ as $- 1 (39)$ .

$x = \frac{- 9 \pm \sqrt{- 1 \cdot 39}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (39)}$ as $\sqrt{- 1} \cdot \sqrt{39}$ .

$x = \frac{- 9 \pm \sqrt{- 1} \cdot \sqrt{39}}{2 \cdot 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 9 \pm i \sqrt{39}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 9 \pm i \sqrt{39}}{2}$