How many real solutions are there to 5x^2+6x+4=0?

No real solutions

Step-by-step explanation:

Use the discriminant to determine the number of real solutions to a quadratic equation.  

The general form for a quadratic equation is ax² + bx + c

The discriminant is    b² - 4ac

The following 3 rules apply...

1. If  b² - 4ac > 0, then there are 2 real solutions

2. If  b² - 4ac = 0, then there is one real solution

3. If  b² - 4ac < 0 then there are no real solutions

For this problem,

a = 5

b = 6

c = 4

Plug them into  b² - 4ac

6² - 4(5)(4)

  36 - 80

       -54           so  b² - 4ac < 0 , there are no real solutions  

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