Solve 6x^2-17=0

$$6 x ^ { 2 } - 17 = 0$$

Solve for x

$$x = \frac{\sqrt{102}}{6} \approx 1.683250823$$

$$x = -\frac{\sqrt{102}}{6} \approx -1.683250823$$

Steps by Finding Square Root

Add 17 to both sides. Anything plus zero gives itself.

$$6x^{2}=17$$

Divide both sides by 6.

$$x^{2}=\frac{17}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{102}}{6} x=-\frac{\sqrt{102}}{6}$$

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.

$$6x^{2}-17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-17\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-17\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-17\right)}}{2\times 6}$$

Multiply -24 times -17.

$$x=\frac{0±\sqrt{408}}{2\times 6}$$

Take the square root of 408.

$$x=\frac{0±2\sqrt{102}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±2\sqrt{102}}{12}$$

Now solve the equation x=\frac{0±2\sqrt{102}}{12} when ± is plus.

$$x=\frac{\sqrt{102}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{102}}{12} when ± is minus.

$$x=-\frac{\sqrt{102}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{102}}{6} x=-\frac{\sqrt{102}}{6}$$