Answer :
Hey there! I'm happy to help!
Our quadratic equation is 2x²-x=-4. Quadratics follow the form ax²+bx+c=0, so our a is 2, our b is -1, and our c is 4 (add 4 to both sides so we have 2x²-x+4=0, fitting the format).
The discriminant of a quadratic equation is b²-4ac. Here's how to figure out how many and what kind of solutions the equation has given the quadratic equation. I'll call the discriminant D.
If D>0, there are 2 real roots.
If D=0, there is 1 real root.
If D<0, there are 2 complex roots.
So, let's look at our discriminant.
-1²-4(2×4)
1-4(8)
1-32
-31
Our discriminant is less than 0, so we have 2 complex solutions.
Have a wonderful day! :D