-x^2 + 5x + 1 = -x^2 + 4x + (3 - x^2);

-x^2 + 5x + 1 = -x^2 + 4x + 3 - x^2;

-x^2 + x^2 + x^2 + 5x - 4x + 1 - 3 = 0;

x^2 + x - 2 = 0;

D = 1 - 4 * 1 *(-2) = 1 + 8 = 9;

x1 = (-1 + 3)/2 = 2/2 = 1;

x2 = (-1 - 3)/2 = -4/2 = -2.