0= -1/14 x^2 + 4x +5 i need to solve for x but i don't get it, explain and

Any time you have a fraction within an equation, multiply the entire equation by the denominator to clear the fraction. Since the lead term is negative, we can multiply that away as well
(-14) (0=-1/14x²+4x+5)      [now distribute]

0=x²-56x+70      [try to factor into binomials first]
Since 70 only has prime factors of 2·5·7, there is no combination which equals (-56). Use the quadratic formula, or complete the square. I'll use quadratic:

x=-b+/-√(b²-4ac)
            2a
a=1, b=(-56), c=70

x= -(-56)+/- √((-56)²-4(1)(70)
                  2(1)
x= 56+/- √(3136-280)
              2
x=56+/-√(2856)
             2
x=56+/-√(2³·3·119)
               2

x=56+/-2√(714)
             2

x=28+√714; x=28-√714

What do you mean by that?