#### Answer

$x=-\dfrac{7}{10}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
5\sqrt{4x+1}=3\sqrt{10x+2}
,$ square both sides of the equation and then isolate the variable. Finally, do checking of the solution with the original equation.
$\bf{\text{Solution Details:}}$
Squaring both sides of the equation results to
\begin{array}{l}\require{cancel}
\left( 5\sqrt{4x+1} \right)^2=\left( 3\sqrt{10x+2} \right)^2
\\\\
25(4x+1)=9(10x+2)
.\end{array}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
25(4x)+25(1)=9(10x)+9(2)
\\\\
100x+25=90x+18
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
100x-90x=18-25
\\\\
10x=-7
\\\\
x=-\dfrac{7}{10}
.\end{array}
Upon checking, $
x=-\dfrac{7}{10}
$ satisfies the original equation.