Solve (m^2-1)+2m=5x-2sqrt{6}

$$( { m }^{ 2 } -1)+2m=5x-2 \sqrt{ 6 }$$

Solve for x

$$x=\frac{m^{2}+2m+2\sqrt{6}-1}{5}$$

Steps for Solving Linear Equation

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

$$5x-2\sqrt{6}=m^{2}-1+2m$$

Add 2\sqrt{6} to both sides.

$$5x=m^{2}-1+2m+2\sqrt{6}$$

The equation is in standard form.

$$5x=m^{2}+2m+2\sqrt{6}-1$$

Divide both sides by 5.

$$\frac{5x}{5}=\frac{m^{2}+2m+2\sqrt{6}-1}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x=\frac{m^{2}+2m+2\sqrt{6}-1}{5}$$

Solve for m (complex solution)

$$m=\sqrt{5x+2-2\sqrt{6}}-1$$

$$m=-\sqrt{5x+2-2\sqrt{6}}-1$$

Solve for m

$$m=\sqrt{5x+2-2\sqrt{6}}-1$$

$$m=-\sqrt{5x+2-2\sqrt{6}}-1\text{, }x\geq \frac{2\sqrt{6}-2}{5}$$