Solve the quadratic equation of x

(sin(2a)).x2 - 2.x.(sin(a)+cos(a)) +2 =0

Rewrite $\sin {2a}$ as $2 \sin a \cos a$ and divide everything by 2:

$(\sin a \cos a )x^2 - (\sin a + \cos a)x + 1 = 0$

Apparently this factors to

$(x \sin a - 1)(x \cos a - 1) = 0$.

Solve for x.

Thanks for it Richard. I appreciate it but I still don't get it. Can you explain it further?

What step don't you get?

Trig identity, $\sin 2a = 2 \sin a \cos a$ for all $a$.