Solve 12z^2-245=0

$$12 z ^ { 2 } - 245 = 0$$

Solve for z

$$z = \frac{7 \sqrt{15}}{6} \approx 4.518480571$$

$$z = -\frac{7 \sqrt{15}}{6} \approx -4.518480571$$

Steps by Finding Square Root

Add 245 to both sides. Anything plus zero gives itself.

$$12z^{2}=245$$

Divide both sides by 12.

$$z^{2}=\frac{245}{12}$$

Take the square root of both sides of the equation.

$$z=\frac{7\sqrt{15}}{6} z=-\frac{7\sqrt{15}}{6}$$

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.

$$12z^{2}-245=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -245 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 12\left(-245\right)}}{2\times 12}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 12\left(-245\right)}}{2\times 12}$$

Multiply -4 times 12.

$$z=\frac{0±\sqrt{-48\left(-245\right)}}{2\times 12}$$

Multiply -48 times -245.

$$z=\frac{0±\sqrt{11760}}{2\times 12}$$

Take the square root of 11760.

$$z=\frac{0±28\sqrt{15}}{2\times 12}$$

Multiply 2 times 12.

$$z=\frac{0±28\sqrt{15}}{24}$$

Now solve the equation z=\frac{0±28\sqrt{15}}{24} when ± is plus.

$$z=\frac{7\sqrt{15}}{6}$$

Now solve the equation z=\frac{0±28\sqrt{15}}{24} when ± is minus.

$$z=-\frac{7\sqrt{15}}{6}$$

The equation is now solved.

$$z=\frac{7\sqrt{15}}{6} z=-\frac{7\sqrt{15}}{6}$$