Answer
$g=5$.
Work Step by Step
$\sqrt {3g+1}=\sqrt {7g-19}$
Squaring both sides of the equation, we get
$(\sqrt {3g+1})^{2}=(\sqrt {7g-19})^{2}$
That is, $3g+1=7g-19$
Subtracting $3g$ from both sides, we get
$3g+1-3g=7g-19-3g$
$\implies 1=4g-19$
Adding $19$ to both sides, we obtain
$\implies 20=4g$
Divide both sides by $4$ to get $g=5$.
To check the solution, put $g=5$ in the original equation.
$\sqrt {3(5)+1}=\sqrt {7(5)-19}$
$\implies \sqrt {16}=\sqrt {16}$ Or $4=4$ which is true.
