Solve frac{(sqrt{a^2-b^2})x}{c}=6

$$\frac { ( \sqrt { a ^ { 2 } - b ^ { 2 } } ) x } { c } = 6$$

Solve for a (complex solution)

$$a=-\sqrt{b^{2}+36\times \left(\frac{c}{x}\right)^{2}}$$

$$a=\sqrt{b^{2}+36\times \left(\frac{c}{x}\right)^{2}}\text{, }|arg(\sqrt{\left(\frac{c}{x}\right)^{2}}x)-arg(c)|<\pi \text{ and }x\neq 0\text{ and }c\neq 0$$

Solve for b (complex solution)

$$b=-\sqrt{a^{2}-36\times \left(\frac{c}{x}\right)^{2}}$$

$$b=\sqrt{a^{2}-36\times \left(\frac{c}{x}\right)^{2}}\text{, }|arg(\sqrt{\left(\frac{c}{x}\right)^{2}}x)-arg(c)|<\pi \text{ and }x\neq 0\text{ and }c\neq 0$$

Solve for a

$$a=-\frac{\sqrt{\left(bx\right)^{2}+36c^{2}}}{|x|}$$

$$a=\frac{\sqrt{\left(bx\right)^{2}+36c^{2}}}{|x|}\text{, }\left(x>0\text{ and }c>0\right)\text{ or }\left(x<0\text{ and }c<0\right)$$