Respuesta :

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Solve for y over the real numbers:
12 y^2 = 17 y - 6
Subtract 17 y - 6 from both sides:
12 y^2 - 17 y + 6 = 0
The left hand side factors into a product with two terms:
(3 y - 2) (4 y - 3) = 0
Split into two equations:
3 y - 2 = 0 or 4 y - 3 = 0
Add 2 to both sides:
3 y = 2 or 4 y - 3 = 0
Divide both sides by 3:
y = 2/3 or 4 y - 3 = 0
Add 3 to both sides:
y = 2/3 or 4 y = 3
Divide both sides by 4:
Answer:  y = 2/3 or y = 3/4
Quadratic formula:    -b +/- √b² - 4ac
                                 -------------------------
                                             2a

First...

      12y² = 17y - 6
    - 12y²  - 12y²
-----------------------------------
       0 = -12y² + 17y -6


In the formula...

a = -12
b = 17 
c = -6


Steps:

-17 +/- √(17)² - 4(-12)(-6)           -17 +/- √289 - 4(72)          -17 +/- √289 - 288
       ------------------------------  ⇒  ------------------------------ ⇒  ----------------------------
                   2(-12)                                    -24                                      -24
 


   -17 +/- √1           -17 + 1         -16          2                  -17 -1       -18         3
------------------ ⇒  -------------- = -------- = -------    OR   ----------- = ------- = ------
       -24                     -24             -24          3                    - 24        -24         4




So x can equal 3/4 or 2/3. I'm sorry if my work seems confusing the way I typed it, but I hope this helps you at least a little bit.


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