# How do you solve |y^ { 2} - 84| = 5y?

Jun 4, 2017

See below.

#### Explanation:

$| {y}^{2} - 84 | = 5 y$

${y}^{2} - 84 = 5 y$ and ${y}^{2} - 84 = - 5 y$

So, we set up two quadratics.

${y}^{2} - 5 y - 84 = 0$
$\left(y - 12\right) \left(y + 7\right) = 0$
$y = 12 , - 7$

${y}^{2} + 5 y - 84 = 0$
$\left(y + 12\right) \left(y - 7\right) = 0$
$y = - 12 , 7$

However, since the function is absolute, the right hand side cannot be negative. So, only positive values of $y$ work, namely $12 , 7$.