Question

how may real and imaginary solutions does 2x^2-7x+9=x+1 have?

Answer 1

for two degree equation, you have 2 solutions

Answer 2

You can use the descriminate of the equation to figure out how many solutions there are for a particular quadratic equation. The discriminate is the portion of the quadratic equation \[\sqrt{b^2 - 4ac}\] If your discriminant is greater than zero you have to real solutions. If your discriminant is equal to zero you will have one real solution. And a discriminant of less than zero has two complex solutions.

Since your discrminiant is \[\sqrt{64 - 64} = \sqrt{0}\] you will have one real solution.