This is an expression, not an equation, so it can't be "solved".
However, you may wish to know how to factorise it or find its zeroes.
One way to do this is to use the quadratic formula x=(-b±√(b2-4ac))/2a where a is the x2 coefficient, b the x coefficient and c the constant.
Another way is to make the expression equal to zero and solve algebraically:
0.200x2+1.00x-0.25=0, divide through by 0.200:
x2+5x-1.25=0,
x2+5x=1.25, then complete the square:
x2+5x+6.25=1.25+6.25, (the LHS is a perfect square)
(x+2.5)2=7.5,
x+2.5=±√7.5,
x=-2.5±√7.5, so there are two zeroes: √7.5-2.5 and -(2.5+√7.5).