Answer
$x= 2,x=0.5$.
Work Step by Step
The given expression is
$\Rightarrow 3(4x-5)^2+20=47$
Subtract $20$ from both sides.
$\Rightarrow 3(4x-5)^2+20-20=47-20$
Simplify.
$\Rightarrow 3(4x-5)^2=27$
Divide both sides by $3$.
$\Rightarrow \frac{3(4x-5)^2}{3}=\frac{27}{3}$
Simplify.
$\Rightarrow (4x-5)^2=9$
Use the square root property.
$\Rightarrow 4x-5=\pm\sqrt{9}$
Simplify.
$\Rightarrow 4x-5=\pm 3$
Separate into two equaitons.
$\Rightarrow 4x-5= 3$ and $4x-5=-3$
Add $5$ to each side of both equations.
$\Rightarrow 4x-5+5= 3+5$ and $4x-5+5=-3+5$
Simplify.
$\Rightarrow 4x= 8$ and $4x=2$
Divide each sides of both equations by $4$
$\Rightarrow \frac{4x}{4}= \frac{8}{4}$ and $\frac{4x}{4}=\frac{2}{4}$
Simplify.
$\Rightarrow x= 2$ and $x=0.5$
Check both answers using the graph.
The graph is shown below.