Write out how to get to these solutions

Question

Write out how to get these solutions

real solutions imaginary solutions

One solution __ 6x-9-x^2=0__ _________

Two solutions __x^2-7=3x, 6x^2=1-x__ __x^2+5x+9=0__

x^2+5x+9=0, x^2-7=3x, 6x-9-x^2=0, 6x^2=1-x

Answer 1

To determine how many solutions, you should use the discriminant of the quadratic formula

b²-4ac

If the discriminant is < 0, there are 2 imaginary solutions

If the discriminant is > 0, there are 2 real solutions

If the discriminant is = 0, there is 1 real solutions

Using this as an example

6x-9-x²=0 rewrite it

-x²+6x-9=0

a=-1

b=6

c=-9

(6)²-4(-1)(-9)

36-36=0

There is one real solution