Solve 4x*6x=37.5

$$4x \times 6x=37.5$$

Solve for x

$$x=1.25$$

$$x=-1.25$$

Steps by Finding Square Root

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

$$4x^{2}\times 6=37.5$$

Multiply 4 and 6 to get 24.

$$24x^{2}=37.5$$

Divide both sides by 24.

$$x^{2}=\frac{37.5}{24}$$

Expand \frac{37.5}{24} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{375}{240}$$

Reduce the fraction \frac{375}{240} to lowest terms by extracting and canceling out 15.

$$x^{2}=\frac{25}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{5}{4} x=-\frac{5}{4}$$

Steps Using the Quadratic Formula

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

$$4x^{2}\times 6=37.5$$

Multiply 4 and 6 to get 24.

$$24x^{2}=37.5$$

Subtract 37.5 from both sides.

$$24x^{2}-37.5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 24 for a, 0 for b, and -37.5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 24\left(-37.5\right)}}{2\times 24}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 24\left(-37.5\right)}}{2\times 24}$$

Multiply -4 times 24.

$$x=\frac{0±\sqrt{-96\left(-37.5\right)}}{2\times 24}$$

Multiply -96 times -37.5.

$$x=\frac{0±\sqrt{3600}}{2\times 24}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\times 24}$$

Multiply 2 times 24.

$$x=\frac{0±60}{48}$$

Now solve the equation x=\frac{0±60}{48} when ± is plus. Reduce the fraction \frac{60}{48} to lowest terms by extracting and canceling out 12.

$$x=\frac{5}{4}$$

Now solve the equation x=\frac{0±60}{48} when ± is minus. Reduce the fraction \frac{-60}{48} to lowest terms by extracting and canceling out 12.

$$x=-\frac{5}{4}$$

The equation is now solved.

$$x=\frac{5}{4} x=-\frac{5}{4}$$