Solve 3b^2-6=0

$$3 b ^ { 2 } - 6 = 0$$

Solve for b

$$b=\sqrt{2}\approx 1.414213562$$

$$b=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Add 6 to both sides. Anything plus zero gives itself.

$$3b^{2}=6$$

Divide both sides by 3.

$$b^{2}=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$b^{2}=2$$

Take the square root of both sides of the equation.

$$b=\sqrt{2} b=-\sqrt{2}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$3b^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 3\left(-6\right)}}{2\times 3}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 3\left(-6\right)}}{2\times 3}$$

Multiply -4 times 3.

$$b=\frac{0±\sqrt{-12\left(-6\right)}}{2\times 3}$$

Multiply -12 times -6.

$$b=\frac{0±\sqrt{72}}{2\times 3}$$

Take the square root of 72.

$$b=\frac{0±6\sqrt{2}}{2\times 3}$$

Multiply 2 times 3.

$$b=\frac{0±6\sqrt{2}}{6}$$

Now solve the equation b=\frac{0±6\sqrt{2}}{6} when ± is plus.

$$b=\sqrt{2}$$

Now solve the equation b=\frac{0±6\sqrt{2}}{6} when ± is minus.

$$b=-\sqrt{2}$$

The equation is now solved.

$$b=\sqrt{2} b=-\sqrt{2}$$