Solve 2.4=(xdiv3)*40x

$$2.4=(x \div 3) \times 40x$$

Solve for x

$$x=\frac{3\sqrt{2}}{10}\approx 0.424264069$$

$$x=-\frac{3\sqrt{2}}{10}\approx -0.424264069$$

Steps by Finding Square Root

Multiply both sides of the equation by 3.

$$7.2=x\times 40x$$

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

$$7.2=x^{2}\times 40$$

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

$$x^{2}\times 40=7.2$$

Divide both sides by 40.

$$x^{2}=\frac{7.2}{40}$$

Expand \frac{7.2}{40} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{72}{400}$$

Reduce the fraction \frac{72}{400} to lowest terms by extracting and canceling out 8.

$$x^{2}=\frac{9}{50}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{2}}{10} x=-\frac{3\sqrt{2}}{10}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 3.

$$7.2=x\times 40x$$

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

$$7.2=x^{2}\times 40$$

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

$$x^{2}\times 40=7.2$$

Subtract 7.2 from both sides.

$$x^{2}\times 40-7.2=0$$

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.

$$40x^{2}-7.2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 40 for a, 0 for b, and -7.2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 40\left(-7.2\right)}}{2\times 40}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 40\left(-7.2\right)}}{2\times 40}$$

Multiply -4 times 40.

$$x=\frac{0±\sqrt{-160\left(-7.2\right)}}{2\times 40}$$

Multiply -160 times -7.2.

$$x=\frac{0±\sqrt{1152}}{2\times 40}$$

Take the square root of 1152.

$$x=\frac{0±24\sqrt{2}}{2\times 40}$$

Multiply 2 times 40.

$$x=\frac{0±24\sqrt{2}}{80}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{80} when ± is plus.

$$x=\frac{3\sqrt{2}}{10}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{80} when ± is minus.

$$x=-\frac{3\sqrt{2}}{10}$$

The equation is now solved.

$$x=\frac{3\sqrt{2}}{10} x=-\frac{3\sqrt{2}}{10}$$