Solve 3x^2-17+1=0

$$3 { x }^{ 2 } -17+1=0$$

Solve for x

$$x = \frac{4 \sqrt{3}}{3} \approx 2.309401077$$

$$x = -\frac{4 \sqrt{3}}{3} \approx -2.309401077$$

Steps by Finding Square Root

Add -17 and 1 to get -16.

$$3x^{2}-16=0$$

Add 16 to both sides. Anything plus zero gives itself.

$$3x^{2}=16$$

Divide both sides by 3.

$$x^{2}=\frac{16}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{3}}{3} x=-\frac{4\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Add -17 and 1 to get -16.

$$3x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-16\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-16\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-16\right)}}{2\times 3}$$

Multiply -12 times -16.

$$x=\frac{0±\sqrt{192}}{2\times 3}$$

Take the square root of 192.

$$x=\frac{0±8\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±8\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{6} when ± is plus.

$$x=\frac{4\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{6} when ± is minus.

$$x=-\frac{4\sqrt{3}}{3}$$

The equation is now solved.

$$x=\frac{4\sqrt{3}}{3} x=-\frac{4\sqrt{3}}{3}$$