Solve 15div100*9600div3*x^2=460

$$15 \div 100 \times 9600 \div 3 \times { x }^{ 2 } =460$$

Solve for x

$$x=\frac{\sqrt{138}}{12}\approx 0.97894501$$

$$x=-\frac{\sqrt{138}}{12}\approx -0.97894501$$

Steps by Finding Square Root

Multiply both sides of the equation by 3.

$$\frac{15}{100}\times 9600x^{2}=1380$$

Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{3}{20}\times 9600x^{2}=1380$$

Multiply \frac{3}{20} and 9600 to get 1440.

$$1440x^{2}=1380$$

Divide both sides by 1440.

$$x^{2}=\frac{1380}{1440}$$

Reduce the fraction \frac{1380}{1440} to lowest terms by extracting and canceling out 60.

$$x^{2}=\frac{23}{24}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{138}}{12} x=-\frac{\sqrt{138}}{12}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 3.

$$\frac{15}{100}\times 9600x^{2}=1380$$

Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{3}{20}\times 9600x^{2}=1380$$

Multiply \frac{3}{20} and 9600 to get 1440.

$$1440x^{2}=1380$$

Subtract 1380 from both sides.

$$1440x^{2}-1380=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1440 for a, 0 for b, and -1380 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1440\left(-1380\right)}}{2\times 1440}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1440\left(-1380\right)}}{2\times 1440}$$

Multiply -4 times 1440.

$$x=\frac{0±\sqrt{-5760\left(-1380\right)}}{2\times 1440}$$

Multiply -5760 times -1380.

$$x=\frac{0±\sqrt{7948800}}{2\times 1440}$$

Take the square root of 7948800.

$$x=\frac{0±240\sqrt{138}}{2\times 1440}$$

Multiply 2 times 1440.

$$x=\frac{0±240\sqrt{138}}{2880}$$

Now solve the equation x=\frac{0±240\sqrt{138}}{2880} when ± is plus.

$$x=\frac{\sqrt{138}}{12}$$

Now solve the equation x=\frac{0±240\sqrt{138}}{2880} when ± is minus.

$$x=-\frac{\sqrt{138}}{12}$$

The equation is now solved.

$$x=\frac{\sqrt{138}}{12} x=-\frac{\sqrt{138}}{12}$$