# How do you solve sqrt( 5x+9) + 3 = 2x?

Aug 3, 2016

$\sqrt{5 x + 9} = 2 x - 3$

${\left(\sqrt{5 x + 9}\right)}^{2} = {\left(2 x - 3\right)}^{2}$

$5 x + 9 = 4 {x}^{2} - 12 x + 9$

$0 = 4 {x}^{2} - 17 x$

$0 = x \left(4 x - 17\right)$

$x = 0 \mathmr{and} \frac{17}{4}$

Checking in the original equation we find the $x = 0$ is extraneous. Hence, the solution set is $\left\{\frac{17}{4}\right\}$.

Hopefully this helps!