Your are given the equation [tex]2x^2 - kx +50 = 0[/tex]. Recall that the solution to the equation [tex]ax^2 +bx +c = 0[/tex] is [tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a} [/tex],
which is known as the quadratic formula.
Using this formula, where [tex]a = 2, b = -k, c= 50[/tex], we have
[tex]x = \frac{-(-k) \pm \sqrt{(-k)^2-4(2)(50)} }{2(2)} = \frac{k\pm \sqrt{k^2-400}}{4}= \frac{k \pm \sqrt{(k-20)(k+20)}}{4}[/tex]