Question

How do you solve for y in `6y^2-5y=6`?

Answer 1

`color(blue)(y=3/2, -2/3`

Explanation:

`6y^2-5y=6`

`6y^2-5y-6=0`

`6y^2-9y+4y-6=0`

`3y(2y-3)+2(2y-3)=0`

`(2y-3)(3y+2)=0`

`therefore 2y-3=0 or 3y+2=0`

`thus, y=3/2, -2/3`

Do not forget to check your answer:
Plug in `color(teal)(y=3/2` and `color(teal)(y=-2/3` in the equation.

`6(3/2)^2-5(3/2)=6*9/4-15/2=27/2-15/2=12/2=6`
That proves that `color(teal)(y=3/2` is correct

Next, check for `-2/3:`
`6(-2/3)^2-5(-2/3)=6*4/9+10/3=8/3+10/3=18/3=6`

That's it your final answer is:
`color(blue)(y=3/2, -2/3`

Answer 2

`y=2/3`
`y=-3/2`

Explanation:

Given -

`6y^2-5y=6`
divide both sides by 6

`y^2-5/6y=1`

`y^2-5/6y+25/144=1+25/144=(144+25)/144=169/144`

`(y+5/12)^2=169/144`

`y+5/12=+-sqrt(169/144)=+-13/12`

`y=13/12-5/12=8/12=2/3`

`y=-13/12-5/12=-18/12=-3/2`