Squaring both sides of the equation to get rid of the square root:

[tex]-x^{2}-x+30 = (2x-10)^{2}[/tex]
[tex]-x^{2}-x+30 = 4x^{2}-40x+100[/tex]
[tex]0 = 5x^{2}-39x+70[/tex]

Solving the quadratic equation:

[tex]5x^{2}-39x+70 = 0[/tex]
tex(x-5) = 0[/tex]

Setting each factor to zero:

[tex]5x-14 = 0[/tex]
[tex]5x = 14[/tex]
[tex]x = \frac{14}{5}[/tex]

or

[tex]x - 5 = 0[/tex]
[tex]x = 5[/tex]

Therefore, the solutions for x are x = 14/5 or x = 5.