Solve for b -4+3b^2=143

$- 4 + 3 b^{2} = 143$

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

Add $4$ to both sides of the equation.

$3 b^{2} = 143 + 4$

Add $143$ and $4$ .

$3 b^{2} = 147$

Divide each term in $3 b^{2} = 147$ by $3$ and simplify.

Divide each term in $3 b^{2} = 147$ by $3$ .

$\frac{3 b^{2}}{3} = \frac{147}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 b^{2}}{3} = \frac{147}{3}$

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

$b^{2} = \frac{147}{3}$

Simplify the right side.

Divide $147$ by $3$ .

$b^{2} = 49$

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

$b = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$b = \pm \sqrt{7^{2}}$

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

$b = \pm 7$

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.

$b = 7$

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

$b = - 7$

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

$b = 7, - 7$