Question

Solve the following equation:
$\sqrt{x+4}-\sqrt{2x+6}=7$

Answer 1

squaring on both sides

$⟹(x+4)+(2x+6)-2\sqrt{(x+4)}\sqrt{(2x+6)}=49$

$⟹2\sqrt{(2x^2+14x+24)}=3x-39$

Squaring on both sides

$8x^2+56x+96=9x^2-234x+1521$

$⟹x=5,285$

(Considering Negative solutions of Square roots)