Solve (5x3/sqrt{m^2+4})sqrt{2}=sqrt{9+5-m^2}

$$( 5 x \frac { 3 } { \sqrt { m ^ { 2 } + 4 } } ) \sqrt { 2 } = \sqrt { 9 + 5 - m ^ { 2 } }$$

Solve for x

$$x=\frac{\sqrt{112+20m^{2}-2m^{4}}}{30}$$

$$|m|\leq \sqrt{14}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{15\sqrt{2}}{\sqrt{m^{2}+4}}x=\sqrt{14-m^{2}}$$

Divide both sides by 15\left(\sqrt{m^{2}+4}\right)^{-1}\sqrt{2}.

$$\frac{\frac{15\sqrt{2}}{\sqrt{m^{2}+4}}x\sqrt{m^{2}+4}}{15\sqrt{2}}=\frac{\sqrt{14-m^{2}}\sqrt{m^{2}+4}}{15\sqrt{2}}$$

Dividing by 15\left(\sqrt{m^{2}+4}\right)^{-1}\sqrt{2} undoes the multiplication by 15\left(\sqrt{m^{2}+4}\right)^{-1}\sqrt{2}.

$$x=\frac{\sqrt{14-m^{2}}\sqrt{m^{2}+4}}{15\sqrt{2}}$$

Divide \sqrt{14-m^{2}} by 15\left(\sqrt{m^{2}+4}\right)^{-1}\sqrt{2}.

$$x=\frac{\sqrt{2\left(14-m^{2}\right)\left(m^{2}+4\right)}}{30}$$

Solve for m

$$\left\{\begin{matrix}m=\sqrt{3\sqrt{9-50x^{2}}+5}\text{; }m=-\sqrt{3\sqrt{9-50x^{2}}+5}\text{, }&x\geq 0\text{ and }x\leq \frac{3\sqrt{2}}{10}\\m=\sqrt{-3\sqrt{9-50x^{2}}+5}\text{; }m=-\sqrt{-3\sqrt{9-50x^{2}}+5}\text{, }&x\geq \frac{2\sqrt{7}}{15}\text{ and }x\leq \frac{3\sqrt{2}}{10}\end{matrix}\right.$$