ANSWER
The exact solution are:
[tex]y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5} [/tex]
EXPLANATION
The given quadratic equation is
[tex] {(5y + 6)}^{2} = 24[/tex]
We use the square root method to solve for y.
We take square root of both sides to get:
[tex] \sqrt{{(5y + 6)}^{2}} = \pm\sqrt{24} [/tex]
This gives us:
[tex]5y + 6 = \pm 2 \sqrt{6} [/tex]
Add -6 to both sides to get:
[tex]5y = - 6 \pm 2 \sqrt{6} [/tex]
Divide through by 5:
[tex]y = \frac{ - 6 \pm2 \sqrt{6} }{5} [/tex]
[tex]y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5} [/tex]
