$$ \sqrt { 2x+3 }+5-3x=0 $$
$$ \sqrt { 2x+3 } = 3x-5 $$
$$ 2x+3 = { (3x-5)}^{ 2 } $$
$$ 2x+3 = { 9x}^{2}-30x+25 $$
$$ { -9x}^{2}+32x = 22 $$
$$ { x}^{2}-\frac {32}{9}x = -\frac {22}{9} $$
$$ { x}^{2}-\frac {32}{9}x + { (-\frac {16}{9})^{ 2 } = (-\frac {16}{9}})^{ 2 } -\frac {22}{9} $$
$$ ({ x}-\frac {16}{9})^{ 2 } =\frac {58}{81} $$
$$ { x}-\frac {16}{9} =\pm \sqrt { \frac {58}{81}} $$
