The equation -3=x^2+4x+1 can be rearranged into x^2+4x+4=0, you should be able recognise that this is an equation of the form ax^2+bx+c (where a, b, and c are constants). The question tells you that the discriminant of an equation of form ax^2+bx+c is equal to b^2-4ac, therefore after rearranging the equation you simply substitute the numbers in:
a=1 b=4 c=4
b^2-4ac=(4)^2-4x(1)x(4)=16-16=0
Therefore the discriminant value is 0.
To determine the amount of real solutions an equation has you look at the discriminant, if the discriminant is less than 0 there are no real solutions, if the discriminant is equal to 0 there is one solution, and if the discriminant is more than 0 there are 2 solutions. therefore as our discriminant is equal to - there is 1 real solution.
