Solve -48x^2+336=0

$$- 48 x ^ { 2 } + 336 = 0$$

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

Subtract 336 from both sides. Anything subtracted from zero gives its negation.

$$-48x^{2}=-336$$

Divide both sides by -48.

$$x^{2}=\frac{-336}{-48}$$

Divide -336 by -48 to get 7.

$$x^{2}=7$$

Take the square root of both sides of the equation.

$$x=\sqrt{7} x=-\sqrt{7}$$

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.

$$-48x^{2}+336=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -48 for a, 0 for b, and 336 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-48\right)\times 336}}{2\left(-48\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-48\right)\times 336}}{2\left(-48\right)}$$

Multiply -4 times -48.

$$x=\frac{0±\sqrt{192\times 336}}{2\left(-48\right)}$$

Multiply 192 times 336.

$$x=\frac{0±\sqrt{64512}}{2\left(-48\right)}$$

Take the square root of 64512.

$$x=\frac{0±96\sqrt{7}}{2\left(-48\right)}$$

Multiply 2 times -48.

$$x=\frac{0±96\sqrt{7}}{-96}$$

Now solve the equation x=\frac{0±96\sqrt{7}}{-96} when ± is plus.

$$x=-\sqrt{7}$$

Now solve the equation x=\frac{0±96\sqrt{7}}{-96} when ± is minus.

$$x=\sqrt{7}$$

The equation is now solved.

$$x=-\sqrt{7} x=\sqrt{7}$$