SOLUTION: I understand how to use the quadratic formula when i'm asked to solve an problem that's straight forward like: x^2+8x+15=0, i can figure out that the answer is {-2/3,4}. I cant un

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Question 297684: I understand how to use the quadratic formula when i'm asked to solve an problem that's straight forward like: x^2+8x+15=0, i can figure out that the answer is {-2/3,4}. I cant understand how to solve the following problem using the quadratic formula:
z^2/1=z/5+6/5
I'm not sure if it's because it involves fractions and i just get really nervous but i'm not sure how to go about solving this problem...
Found 3 solutions by Fombitz, Alan3354, richwmiller:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!


You can multiply by the LCD to get rid of the fractions, in this case by 5.

Then , , .




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Or you can just move forward with the fractions.


, , .








You'll get to the same place.
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and
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Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
z^2/1=z/5+6/5
Step 1, eliminate fractions.
Multiply thru by 5
5z^2 = z + 6
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
This one can be factored too once you get it in the right form.
z=-1 and 6/5
First multiply through by 5
5z^2=z+6
5z^-z-6=0
We need factors of -30 which add up to -1
-6 and 5
5z^2-6z+5z-6=0
rearrange
5z^2+5z-6z-6
5z*(z+1)-6(z+1)=0
(5z-6)*(z+1)=0
Now the quadratic formula with the form 5z^2-x-6=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=121 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.2, -1. Here's your graph:
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