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

2 Answers
Candy
May 25, 2018

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

Nallasivam V
May 25, 2018

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

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