Best solutions to - "How do you solve for y in 6y2−5y=6?"

High School
Algebra
Algebra I
Quadratic function and equation

maliaseth0

Answered question

2022-01-22

How do you solve for y in

6 y^{2} - 5 y = 6

Answer & Explanation

Flickkorbma

Beginner2022-01-23Added 17 answers

Step 1
$6 y^{2} - 5 y = 6$
$6 y^{2} - 5 y - 6 = 0$
$6 y^{2} - 9 y + 4 y - 6 = 0$
$3 y (2 y - 3) + 2 (2 y - 3) = 0$
$(2 y - 3) (3 y + 2) = 0$
$∴ 2 y - 3 = 0$ or $3 y + 2 = 0$
thus, $y = \frac{3}{2}, - \frac{2}{3}$
Do not forget to check your answer:
Plug in $y = \frac{3}{2}$ and $y = - \frac{2}{3}$ in the equation.
$6 {(\frac{3}{2})}^{2} - 5 (\frac{3}{2})$
$= 6 \times \frac{9}{4} - \frac{15}{2}$
$= \frac{27}{2} - \frac{15}{2}$
$- \frac{12}{2} = 6$
That proves that $y = \frac{3}{2}$ is correct
Next, check for $- \frac{2}{3}$
$6 {(- \frac{2}{3})}^{2} - 5 (- \frac{2}{3})$
$= 6 \times \frac{4}{9} + \frac{10}{3}$
$= \frac{8}{3} + \frac{10}{3}$
$= \frac{18}{3} = 6$
That's it your final answer is:
$y = \frac{3}{2}, - \frac{2}{3}$

immablondevl

Beginner2022-01-24Added 11 answers

Step 1
Given:

6 y^{2} - 5 y = 6

divide both sides by 6

y^{2} - \frac{5}{6} y = 1

y^{2} - \frac{5}{6} y + \frac{25}{144}

= 1 + \frac{25}{144}

= \frac{144 + 25}{144}

= \frac{169}{144}

{(y + \frac{5}{12})}^{2} = \frac{169}{144}

y + \frac{5}{12} = \pm \sqrt{\frac{169}{144}} = \pm \frac{13}{12}

y = \frac{13}{12} - \frac{5}{12} = \frac{8}{12} = \frac{2}{3}

y = - \frac{13}{12} - \frac{5}{12} = - \frac{18}{12} = - \frac{3}{2}

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Algebra I

Didn't find what you were looking for?