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48000^{3}=\frac{10000}{408321}x^{2}\times 19600^{3}
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.
110592000000000=\frac{10000}{408321}x^{2}\times 19600^{3}
Calculate 48000 to the power of 3 and get 110592000000000.
110592000000000=\frac{10000}{408321}x^{2}\times 7529536000000
Calculate 19600 to the power of 3 and get 7529536000000.
110592000000000=\frac{75295360000000000}{408321}x^{2}
Multiply \frac{10000}{408321} and 7529536000000 to get \frac{75295360000000000}{408321}.
\frac{75295360000000000}{408321}x^{2}=110592000000000
Swap sides so that all variable terms are on the left hand side.
x^{2}=\frac{110592000000000}{\frac{75295360000000000}{408321}}
Divide both sides by \frac{75295360000000000}{408321}.
x=\frac{7668\sqrt{30}}{1715} x=-\frac{7668\sqrt{30}}{1715}
Take the square root of both sides of the equation.
48000^{3}=\frac{10000}{408321}x^{2}\times 19600^{3}
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.
110592000000000=\frac{10000}{408321}x^{2}\times 19600^{3}
Calculate 48000 to the power of 3 and get 110592000000000.
110592000000000=\frac{10000}{408321}x^{2}\times 7529536000000
Calculate 19600 to the power of 3 and get 7529536000000.
110592000000000=\frac{75295360000000000}{408321}x^{2}
Multiply \frac{10000}{408321} and 7529536000000 to get \frac{75295360000000000}{408321}.
\frac{75295360000000000}{408321}x^{2}=110592000000000
Swap sides so that all variable terms are on the left hand side.
\frac{75295360000000000}{408321}x^{2}-110592000000000=0
Subtract 110592000000000 from both sides.
x=\frac{0±\sqrt{0^{2}-4\times \frac{75295360000000000}{408321}\left(-110592000000000\right)}}{2\times \frac{75295360000000000}{408321}}
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{-4\times \frac{75295360000000000}{408321}\left(-110592000000000\right)}}{2\times \frac{75295360000000000}{408321}}
Square 0.
x=\frac{0±\sqrt{-\frac{301181440000000000}{408321}\left(-110592000000000\right)}}{2\times \frac{75295360000000000}{408321}}
Multiply -4 times \frac{75295360000000000}{408321}.
x=\frac{0±\sqrt{\frac{1233639178240000000000000000000}{15123}}}{2\times \frac{75295360000000000}{408321}}
Multiply -\frac{301181440000000000}{408321} times -110592000000000.
x=\frac{0±\frac{351232000000000\sqrt{30}}{213}}{2\times \frac{75295360000000000}{408321}}
Take the square root of \frac{1233639178240000000000000000000}{15123}.
x=\frac{0±\frac{351232000000000\sqrt{30}}{213}}{\frac{150590720000000000}{408321}}
Multiply 2 times \frac{75295360000000000}{408321}.
x=\frac{7668\sqrt{30}}{1715}
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} x=-\frac{7668\sqrt{30}}{1715}
The equation is now solved.