Solve x/15*x/20=10

$$\frac { x } { 15 } \times \frac { x } { 20 } = 10$$

Solve for x

$$x=10\sqrt{30}\approx 54.772255751$$

$$x=-10\sqrt{30}\approx -54.772255751$$

Steps by Finding Square Root

Multiply both sides of the equation by 60, the least common multiple of 15,20.

$$4x\times \frac{x}{20}=600$$

Cancel out 20, the greatest common factor in 4 and 20.

$$\frac{x}{5}x=600$$

Express \frac{x}{5}x as a single fraction.

$$\frac{xx}{5}=600$$

Multiply both sides by 5.

$$xx=600\times 5$$

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

$$x^{2}=600\times 5$$

Multiply 600 and 5 to get 3000.

$$x^{2}=3000$$

Take the square root of both sides of the equation.

$$x=10\sqrt{30} x=-10\sqrt{30}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 60, the least common multiple of 15,20.

$$4x\times \frac{x}{20}=600$$

Cancel out 20, the greatest common factor in 4 and 20.

$$\frac{x}{5}x=600$$

Express \frac{x}{5}x as a single fraction.

$$\frac{xx}{5}=600$$

Subtract 600 from both sides.

$$\frac{xx}{5}-600=0$$

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

$$\frac{x^{2}}{5}-600=0$$

Multiply both sides of the equation by 5.

$$x^{2}-3000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3000\right)}}{2}$$

Multiply -4 times -3000.

$$x=\frac{0±\sqrt{12000}}{2}$$

Take the square root of 12000.

$$x=\frac{0±20\sqrt{30}}{2}$$

Now solve the equation x=\frac{0±20\sqrt{30}}{2} when ± is plus.

$$x=10\sqrt{30}$$

Now solve the equation x=\frac{0±20\sqrt{30}}{2} when ± is minus.

$$x=-10\sqrt{30}$$

The equation is now solved.

$$x=10\sqrt{30} x=-10\sqrt{30}$$