Solve 625/x-x/3=0

$$\frac{ 625 }{ x } - \frac{ x }{ 3 } =0$$

Solve for x

$$x=25\sqrt{3}\approx 43.301270189$$

$$x=-25\sqrt{3}\approx -43.301270189$$

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 3x, the least common multiple of x,3.

$$3\times 625-xx=0$$

Multiply x and x to get x^{2}.

$$3\times 625-x^{2}=0$$

Multiply 3 and 625 to get 1875.

$$1875-x^{2}=0$$

Subtract 1875 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-1875$$

Divide both sides by -1.

$$x^{2}=\frac{-1875}{-1}$$

Fraction \frac{-1875}{-1} can be simplified to 1875 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=1875$$

Take the square root of both sides of the equation.

$$x=25\sqrt{3} x=-25\sqrt{3}$$

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 3x, the least common multiple of x,3.

$$3\times 625-xx=0$$

Multiply x and x to get x^{2}.

$$3\times 625-x^{2}=0$$

Multiply 3 and 625 to get 1875.

$$1875-x^{2}=0$$

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.

$$-x^{2}+1875=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 1875 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 1875}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 1875}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 1875}}{2\left(-1\right)}$$

Multiply 4 times 1875.

$$x=\frac{0±\sqrt{7500}}{2\left(-1\right)}$$

Take the square root of 7500.

$$x=\frac{0±50\sqrt{3}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±50\sqrt{3}}{-2}$$

Now solve the equation x=\frac{0±50\sqrt{3}}{-2} when ± is plus.

$$x=-25\sqrt{3}$$

Now solve the equation x=\frac{0±50\sqrt{3}}{-2} when ± is minus.

$$x=25\sqrt{3}$$

The equation is now solved.

$$x=-25\sqrt{3} x=25\sqrt{3}$$