Solving $8=x(2(1-\sqrt{5}))+(1-x)(2(1+\sqrt{5}))$ I came up with this equation during my homework :
$8=x(2(1-\sqrt{5}))+(1-x)(2(1+\sqrt{5}))$
My algebra is weak and I can't seem to find a way to solve for x nicely 
Could someone please show me a decent way of doing this? 
Thanks alot, Jason

$$8 = x\left [ 2-2\sqrt{5} \right ] + \left ( 1 - x \right )\left [ 2 + 2\sqrt{5} \right ]$$
use foil 
$$8 = 2x - 2x\sqrt{5} + 2 + 2\sqrt{5} - 2x - 2x\sqrt{5}$$
$$8 = -4x\sqrt{5} + 2\sqrt{5} + 2$$
subtract 2 and square both sides
$$36 = 16x^25 + 20$$
subtract 20 from both sides to obtain
$$80x^2 = 16$$
Now divide both sides by 80 and you get $$x^2 = 16/80$$
therefore $$x = \pm 1 / \sqrt{5}$$
