Answer:[tex]x=6,-0.75[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{x+3}=\sqrt{5x+6}-3[/tex]
[tex]\sqrt{x+3}+3=\sqrt{5x+6}[/tex]
Squaring both sides
[tex]x+3+9+6\times \sqrt{x+3}=5x+6[/tex]
[tex]x+12+6\times \sqrt{x+3}=5x+6[/tex]
[tex]6\times \sqrt{x+3}=4x-6[/tex]
[tex]3\times \sqrt{x+3}=2x-3[/tex]
[tex]4x^2-21x-18=0[/tex]
[tex]x=\frac{21\pm \sqrt{21^2}+4\times 18\times 4}{2\times 4}[/tex]
[tex]x=6,-0.75[/tex]
