Solve 4m3-2x^2=1

$$4m3-2 { x }^{ 2 } = 1$$

Solve for m_3

$$m_{3}=\frac{x^{2}}{2}+\frac{1}{4}$$

Steps for Solving Linear Equation

Add 2x^{2} to both sides.

$$4m_{3}=1+2x^{2}$$

The equation is in standard form.

$$4m_{3}=2x^{2}+1$$

Divide both sides by 4.

$$\frac{4m_{3}}{4}=\frac{2x^{2}+1}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$m_{3}=\frac{2x^{2}+1}{4}$$

Divide 1+2x^{2} by 4.

$$m_{3}=\frac{x^{2}}{2}+\frac{1}{4}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{8m_{3}-2}}{2}$$

$$x=\frac{\sqrt{8m_{3}-2}}{2}$$

Solve for x

$$x=\frac{\sqrt{8m_{3}-2}}{2}$$

$$x=-\frac{\sqrt{8m_{3}-2}}{2}\text{, }m_{3}\geq \frac{1}{4}$$