Solve for x 5-3x^2=-7

$5 - 3 x^{2} = - 7$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$- 3 x^{2} = - 7 - 5$

Subtract $5$ from $- 7$ .

$- 3 x^{2} = - 12$

Step 2

Divide each term in $- 3 x^{2} = - 12$ by $- 3$ and simplify.

Divide each term in $- 3 x^{2} = - 12$ by $- 3$ .

$\frac{- 3 x^{2}}{- 3} = \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x^{2}}{- 3} = \frac{- 12}{- 3}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 12}{- 3}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$x^{2} = 4$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{4}$

Step 4

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$x = \pm \sqrt{2^{2}}$

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

$x = \pm 2$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2, - 2$