Respuesta :
The value of y is, [tex]y=\frac{2\sqrt{6}-6}{5},\:y=\frac{-2\sqrt{6}-6}{5}[/tex]
We have given that,
[tex]\left(5y+6\right)^2=24[/tex]
We have to determine the value of y,
What is the formula for the quadratic equation?
[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
Therefore,we get
[tex]5y+6=\sqrt{24}[/tex]
[tex]5y+6=2\sqrt{6}[/tex]
[tex]\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}[/tex]
[tex]5y+6-6=2\sqrt{6}-6[/tex]
[tex]5y=2\sqrt{6}-6[/tex]
[tex]\frac{5y}{5}=\frac{2\sqrt{6}}{5}-\frac{6}{5}[/tex]
[tex]y=\frac{2\sqrt{6}-6}{5}[/tex]
[tex]y=\frac{2\sqrt{6}-6}{5},\:y=\frac{-2\sqrt{6}-6}{5}[/tex]
Therefore the value of y is,
[tex]y=\frac{2\sqrt{6}-6}{5},\:y=\frac{-2\sqrt{6}-6}{5}[/tex]
To learn more about the quadratic equation visit:
https://brainly.com/question/1214333
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