Please help?

Question

Find all real solutions to the equation

1. √5x-x² = √6

Write answers in the form a + bi

2. ) 4-√-12/2

Find the imaginary solutions to the equation

3. ) 2b²+9=0

Thank you

Answer 1

sqrt(5x-x^2= sqrt6
5x-x^2>=0 so 0<=x<=5
squaring
5x-x^2=6 so x^2-5x+6=0 and
x=((5+-1)/2
x=3 and x=2
sqrt(-12) = i*2sqrt3
so2) = 4-i sqrt 3
3) b=+-3/2sqrt2*i

Answer 2

2b²+9=0
2b^2 = -9
b^2 = -9/2
b = +/-i 3/sqrt(2)