Solve for a 159=-3+2a^2

$159 = - 3 + 2 a^{2}$

Rewrite the equation as $- 3 + 2 a^{2} = 159$ .

$- 3 + 2 a^{2} = 159$

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

Add $3$ to both sides of the equation.

$2 a^{2} = 159 + 3$

Add $159$ and $3$ .

$2 a^{2} = 162$

Divide each term in $2 a^{2} = 162$ by $2$ and simplify.

Divide each term in $2 a^{2} = 162$ by $2$ .

$\frac{2 a^{2}}{2} = \frac{162}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a^{2}}{2} = \frac{162}{2}$

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

$a^{2} = \frac{162}{2}$

Simplify the right side.

Divide $162$ by $2$ .

$a^{2} = 81$

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

$a = \pm \sqrt{81}$

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$a = \pm \sqrt{9^{2}}$

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

$a = \pm 9$

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.

$a = 9$

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

$a = - 9$

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

$a = 9, - 9$