Solve 19600^3/6.39^2=48000^3/x^2

$$\frac{ { 19600 }^{ 3 } }{ { 6.39 }^{ 2 } } = \frac{ { 48000 }^{ 3 } }{ { x }^{ 2 } }$$

Solve for x

$$x = \frac{7668 \sqrt{30}}{1715} \approx 24.48942607$$

$$x = -\frac{7668 \sqrt{30}}{1715} \approx -24.48942607$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$\frac{10000}{408321}x^{2}\times 19600^{3}=48000^{3}$$

Calculate 19600 to the power of 3 and get 7529536000000.

$$\frac{10000}{408321}x^{2}\times 7529536000000=48000^{3}$$

Multiply \frac{10000}{408321} and 7529536000000 to get \frac{75295360000000000}{408321}.

$$\frac{75295360000000000}{408321}x^{2}=48000^{3}$$

Calculate 48000 to the power of 3 and get 110592000000000.

$$\frac{75295360000000000}{408321}x^{2}=110592000000000$$

Divide both sides by \frac{75295360000000000}{408321}.

$$x^{2}=\frac{110592000000000}{\frac{75295360000000000}{408321}}$$

Take the square root of both sides of the equation.

$$x=\frac{7668\sqrt{30}}{1715} x=-\frac{7668\sqrt{30}}{1715}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$\frac{10000}{408321}x^{2}\times 19600^{3}=48000^{3}$$

Calculate 19600 to the power of 3 and get 7529536000000.

$$\frac{10000}{408321}x^{2}\times 7529536000000=48000^{3}$$

Multiply \frac{10000}{408321} and 7529536000000 to get \frac{75295360000000000}{408321}.

$$\frac{75295360000000000}{408321}x^{2}=48000^{3}$$

Calculate 48000 to the power of 3 and get 110592000000000.

$$\frac{75295360000000000}{408321}x^{2}=110592000000000$$

Subtract 110592000000000 from both sides.

$$\frac{75295360000000000}{408321}x^{2}-110592000000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{75295360000000000}{408321} for a, 0 for b, and -110592000000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{75295360000000000}{408321}\left(-110592000000000\right)}}{2\times \frac{75295360000000000}{408321}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{75295360000000000}{408321}\left(-110592000000000\right)}}{2\times \frac{75295360000000000}{408321}}$$

Multiply -4 times \frac{75295360000000000}{408321}.

$$x=\frac{0±\sqrt{-\frac{301181440000000000}{408321}\left(-110592000000000\right)}}{2\times \frac{75295360000000000}{408321}}$$

Multiply -\frac{301181440000000000}{408321} times -110592000000000.

$$x=\frac{0±\sqrt{\frac{1233639178240000000000000000000}{15123}}}{2\times \frac{75295360000000000}{408321}}$$

Take the square root of \frac{1233639178240000000000000000000}{15123}.

$$x=\frac{0±\frac{351232000000000\sqrt{30}}{213}}{2\times \frac{75295360000000000}{408321}}$$

Multiply 2 times \frac{75295360000000000}{408321}.

$$x=\frac{0±\frac{351232000000000\sqrt{30}}{213}}{\frac{150590720000000000}{408321}}$$

Now solve the equation x=\frac{0±\frac{351232000000000\sqrt{30}}{213}}{\frac{150590720000000000}{408321}} when ± is plus.

$$x=\frac{7668\sqrt{30}}{1715}$$

Now solve the equation x=\frac{0±\frac{351232000000000\sqrt{30}}{213}}{\frac{150590720000000000}{408321}} when ± is minus.

$$x=-\frac{7668\sqrt{30}}{1715}$$

The equation is now solved.

$$x=\frac{7668\sqrt{30}}{1715} x=-\frac{7668\sqrt{30}}{1715}$$