Solve 0.15=0.001*x^2/15

$$0.15= \frac{ 0.001 \times { x }^{ 2 } }{ 15 }$$

Solve for x

$$x=15\sqrt{10}\approx 47.434164903$$

$$x=-15\sqrt{10}\approx -47.434164903$$

Steps by Finding Square Root

Multiply both sides by 15.

$$0.15\times 15=0.001x^{2}$$

Multiply 0.15 and 15 to get 2.25.

$$2.25=0.001x^{2}$$

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

$$0.001x^{2}=2.25$$

Divide both sides by 0.001.

$$x^{2}=\frac{2.25}{0.001}$$

Expand \frac{2.25}{0.001} by multiplying both numerator and the denominator by 1000. Anything divided by one gives itself.

$$x^{2}=2250$$

Take the square root of both sides of the equation.

$$x=15\sqrt{10} x=-15\sqrt{10}$$

Steps Using the Quadratic Formula

Multiply both sides by 15.

$$0.15\times 15=0.001x^{2}$$

Multiply 0.15 and 15 to get 2.25.

$$2.25=0.001x^{2}$$

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

$$0.001x^{2}=2.25$$

Subtract 2.25 from both sides.

$$0.001x^{2}-2.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.001 for a, 0 for b, and -2.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.001\left(-2.25\right)}}{2\times 0.001}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.001\left(-2.25\right)}}{2\times 0.001}$$

Multiply -4 times 0.001.

$$x=\frac{0±\sqrt{-0.004\left(-2.25\right)}}{2\times 0.001}$$

Multiply -0.004 times -2.25 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{0.009}}{2\times 0.001}$$

Take the square root of 0.009.

$$x=\frac{0±\frac{3\sqrt{10}}{100}}{2\times 0.001}$$

Multiply 2 times 0.001.

$$x=\frac{0±\frac{3\sqrt{10}}{100}}{0.002}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{10}}{100}}{0.002} when ± is plus.

$$x=15\sqrt{10}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{10}}{100}}{0.002} when ± is minus.

$$x=-15\sqrt{10}$$

The equation is now solved.

$$x=15\sqrt{10} x=-15\sqrt{10}$$