Solve 5x^2/2=54

$$\frac { 5 x ^ { 2 } } { 2 } = 54$$

Solve for x

$$x = \frac{6 \sqrt{15}}{5} \approx 4.647580015$$

$$x = -\frac{6 \sqrt{15}}{5} \approx -4.647580015$$

Steps by Finding Square Root

Multiply both sides by 2.

$$5x^{2}=54\times 2$$

Multiply 54 and 2 to get 108.

$$5x^{2}=108$$

Divide both sides by 5.

$$x^{2}=\frac{108}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{6\sqrt{15}}{5} x=-\frac{6\sqrt{15}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$5x^{2}=54\times 2$$

Multiply 54 and 2 to get 108.

$$5x^{2}=108$$

Subtract 108 from both sides.

$$5x^{2}-108=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -108 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-108\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-108\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-108\right)}}{2\times 5}$$

Multiply -20 times -108.

$$x=\frac{0±\sqrt{2160}}{2\times 5}$$

Take the square root of 2160.

$$x=\frac{0±12\sqrt{15}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±12\sqrt{15}}{10}$$

Now solve the equation x=\frac{0±12\sqrt{15}}{10} when ± is plus.

$$x=\frac{6\sqrt{15}}{5}$$

Now solve the equation x=\frac{0±12\sqrt{15}}{10} when ± is minus.

$$x=-\frac{6\sqrt{15}}{5}$$

The equation is now solved.

$$x=\frac{6\sqrt{15}}{5} x=-\frac{6\sqrt{15}}{5}$$