Solve 27m^{2}=3m^2-(m/2+x)^2+frac{6sqrt{3}-1}{2}m-x^2+3m^2

$$27 m ^ { 2 } = 3 m ^ { 2 } - ( \frac { m } { 2 } + x ) ^ { 2 } + \frac { 6 \sqrt { 3 } - 1 } { 2 } m - x ^ { 2 } + 3 m ^ { 2 }$$

Solve for m (complex solution)

$$m=\frac{\sqrt{-676x^{2}-24\sqrt{3}x+4x+109-12\sqrt{3}}-2x+6\sqrt{3}-1}{85}$$

$$m=\frac{-\sqrt{-676x^{2}-24\sqrt{3}x+4x+109-12\sqrt{3}}-2x+6\sqrt{3}-1}{85}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{m\left(-169m+24\sqrt{3}-4\right)}-m}{4}$$

$$x=\frac{\sqrt{m\left(-169m+24\sqrt{3}-4\right)}-m}{4}$$

Solve for m

$$m=\frac{\sqrt{-676x^{2}-24\sqrt{3}x+4x+109-12\sqrt{3}}-2x+6\sqrt{3}-1}{85}$$

$$m=\frac{-\sqrt{-676x^{2}-24\sqrt{3}x+4x+109-12\sqrt{3}}-2x+6\sqrt{3}-1}{85}\text{, }x\geq \frac{\sqrt{170}}{338}-\frac{3\sqrt{3}}{169}-\frac{3\sqrt{510}}{169}+\frac{1}{338}\text{ and }x\leq \frac{3\sqrt{510}}{169}-\frac{\sqrt{170}}{338}-\frac{3\sqrt{3}}{169}+\frac{1}{338}$$

Solve for x

$$x=\frac{-\sqrt{-169m^{2}+24\sqrt{3}m-4m}-m}{4}$$

$$x=\frac{\sqrt{-169m^{2}+24\sqrt{3}m-4m}-m}{4}\text{, }m\geq 0\text{ and }m\leq \frac{24\sqrt{3}-4}{169}$$