SOLUTION: Someone please help. y^2=5/7y+3/7 Does it have 2 non-real solutions, 2 real solutions, or 1 real solutions. Thank you.

Question 132299: Someone please help.
y^2=5/7y+3/7 Does it have 2 non-real solutions, 2 real solutions, or 1 real solutions.
Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Subtract from both sides

Rearrange the terms

Multiply both sides by the LCD 7. This will eliminate the fractions

Distribute and multiply

From the quadratic formula

the discriminant consists of all of the terms in the square root. So the discriminant is

the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.

Now let's find the discriminant for :

Start with the given equation

Plug in a=-7, b=5, c=3

Square 5 to get 25

Multiply -4*-7*3 to get 84

Combine 25 and 84 to get 109

Since the discriminant equals 109 (which is greater than zero) , this means there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.

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