Answer:
[tex]\large\boxed{x=\dfrac{5\pm3\sqrt3}{2}}[/tex]
Step-by-step explanation:
[tex]Domain:\ x-5\neq0\to x\neq5\\\\\dfrac{2}{x-5}=4x\\\\\dfrac{2}{x-5}=\dfrac{4x}{1}\qquad\text{cross multiply}\\\\(4x)(x-5)=(2)(1)\qquad\text{use the distributive property}\\\\(4x)(x)+(4x)(-5)=2\\\\4x^2-20x=2\\\\2^2x^2-20x=2\\\\(2x)^2-2(2x)(5)=2\qquad\text{add}\ 5^2\ \text{to both sides}\\\\(2x)^2-2(2x)(5)+5^2=2+5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(2x-5)^2=2+25\\\\(2x-5)^2=27\to2x-5=\pm\sqrt{27}\qquad\text{add 5 to both sides}[/tex]
[tex]2x=5\pm\sqrt{9\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\2x=5\pm\sqrt9\cdot\sqrt3\\\\2x=5\pm3\sqrt3\qquad\text{divide both sides by 2}\\\\x=\dfrac{5\pm3\sqrt3}{2}[/tex]
