Find the Roots (Zeros) 5x^2+3=83

$5 x^{2} + 3 = 83$

Step 1

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

Subtract $3$ from both sides of the equation.

$5 x^{2} = 83 - 3$

Subtract $3$ from $83$ .

$5 x^{2} = 80$

Step 2

Divide each term in $5 x^{2} = 80$ by $5$ and simplify.

Divide each term in $5 x^{2} = 80$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{80}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{80}{5}$

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

$x^{2} = \frac{80}{5}$

Simplify the right side.

Divide $80$ by $5$ .

$x^{2} = 16$

Step 3

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

$x = \pm \sqrt{16}$

Step 4

Simplify $\pm \sqrt{16}$ .

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

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

$x = \pm 4$

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.

$x = 4$

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

$x = - 4$

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

$x = 4, - 4$

Step 6