Solve 50/2x+15/x=x

$$\frac{ 50 }{ 2x } + \frac{ 15 }{ x } =x$$

Solve for x

$$x=2\sqrt{10}\approx 6.32455532$$

$$x=-2\sqrt{10}\approx -6.32455532$$

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 2x, the least common multiple of 2x,x.

$$50+2\times 15=x\times 2x$$

Multiply 2 and 15 to get 30.

$$50+30=x\times 2x$$

Add 50 and 30 to get 80.

$$80=x\times 2x$$

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

$$80=x^{2}\times 2$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}\times 2=80$$

Divide both sides by 2.

$$x^{2}=\frac{80}{2}$$

Divide 80 by 2 to get 40.

$$x^{2}=40$$

Take the square root of both sides of the equation.

$$x=2\sqrt{10} x=-2\sqrt{10}$$

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 2x, the least common multiple of 2x,x.

$$50+2\times 15=x\times 2x$$

Multiply 2 and 15 to get 30.

$$50+30=x\times 2x$$

Add 50 and 30 to get 80.

$$80=x\times 2x$$

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

$$80=x^{2}\times 2$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}\times 2=80$$

Subtract 80 from both sides.

$$x^{2}\times 2-80=0$$

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.

$$2x^{2}-80=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-80\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-80\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-80\right)}}{2\times 2}$$

Multiply -8 times -80.

$$x=\frac{0±\sqrt{640}}{2\times 2}$$

Take the square root of 640.

$$x=\frac{0±8\sqrt{10}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±8\sqrt{10}}{4}$$

Now solve the equation x=\frac{0±8\sqrt{10}}{4} when ± is plus.

$$x=2\sqrt{10}$$

Now solve the equation x=\frac{0±8\sqrt{10}}{4} when ± is minus.

$$x=-2\sqrt{10}$$

The equation is now solved.

$$x=2\sqrt{10} x=-2\sqrt{10}$$