Solve 3x^2-14-5=0

$$3 { x }^{ 2 } -14-5=0$$

Solve for x

$$x = \frac{\sqrt{57}}{3} \approx 2.516611478$$

$$x = -\frac{\sqrt{57}}{3} \approx -2.516611478$$

Steps by Finding Square Root

Subtract 5 from -14 to get -19.

$$3x^{2}-19=0$$

Add 19 to both sides. Anything plus zero gives itself.

$$3x^{2}=19$$

Divide both sides by 3.

$$x^{2}=\frac{19}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{57}}{3} x=-\frac{\sqrt{57}}{3}$$

Steps Using the Quadratic Formula

Subtract 5 from -14 to get -19.

$$3x^{2}-19=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -19 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-19\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-19\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-19\right)}}{2\times 3}$$

Multiply -12 times -19.

$$x=\frac{0±\sqrt{228}}{2\times 3}$$

Take the square root of 228.

$$x=\frac{0±2\sqrt{57}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{57}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{57}}{6} when ± is plus.

$$x=\frac{\sqrt{57}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{57}}{6} when ± is minus.

$$x=-\frac{\sqrt{57}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{57}}{3} x=-\frac{\sqrt{57}}{3}$$