We can use the discriminant to determine the number and type of solutions.
4x2 + 2x= -3
Rewriting so the solution is equal to zero
4x2 + 2x+3 =0
Using the form
ax^2 +bx +c =0
We can use the discriminant
b^2 -4ac where a=4 b=2 and c = 3
2^2 -4(4)(3)
4 - 48
-44
Since this is <0 there are no real solutions ( there are 2 complex solutions)
if it is >0 there are 2 real solutions
=0 there is one real solution
