Solve 6/x-7x/5=x/10

$$\frac { 6 } { x } - \frac { 7 x } { 5 } = \frac { x } { 10 }$$

Solve for x

$$x=2$$

$$x=-2$$

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 10x, the least common multiple of x,5,10.

$$10\times 6-2x\times 7x=xx$$

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

$$10\times 6-2x\times 7x=x^{2}$$

Multiply 10 and 6 to get 60.

$$60-2x\times 7x=x^{2}$$

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

$$60-2x^{2}\times 7=x^{2}$$

Multiply 2 and 7 to get 14.

$$60-14x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$60-14x^{2}-x^{2}=0$$

Subtract 60 from both sides. Anything subtracted from zero gives its negation.

$$-14x^{2}-x^{2}=-60$$

Combine -14x^{2} and -x^{2} to get -15x^{2}.

$$-15x^{2}=-60$$

Divide both sides by -15.

$$x^{2}=\frac{-60}{-15}$$

Divide -60 by -15 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

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 10x, the least common multiple of x,5,10.

$$10\times 6-2x\times 7x=xx$$

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

$$10\times 6-2x\times 7x=x^{2}$$

Multiply 10 and 6 to get 60.

$$60-2x\times 7x=x^{2}$$

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

$$60-2x^{2}\times 7=x^{2}$$

Multiply 2 and 7 to get 14.

$$60-14x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$60-14x^{2}-x^{2}=0$$

Combine -14x^{2} and -x^{2} to get -15x^{2}.

$$60-15x^{2}=0$$

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.

$$-15x^{2}+60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -15 for a, 0 for b, and 60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\times 60}}{2\left(-15\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)\times 60}}{2\left(-15\right)}$$

Multiply -4 times -15.

$$x=\frac{0±\sqrt{60\times 60}}{2\left(-15\right)}$$

Multiply 60 times 60.

$$x=\frac{0±\sqrt{3600}}{2\left(-15\right)}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\left(-15\right)}$$

Multiply 2 times -15.

$$x=\frac{0±60}{-30}$$

Now solve the equation x=\frac{0±60}{-30} when ± is plus. Divide 60 by -30.

$$x=-2$$

Now solve the equation x=\frac{0±60}{-30} when ± is minus. Divide -60 by -30.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$