Question

x-1= the square root of 3x+7

Answer 1

the x in this equation has ranges,
\[x \ge1\] and \[x \ge-\frac{ 7 }{ 3 }\] becauset there is no negative value of results from square root - ing something
1. square both side \[x - 1 = \sqrt{3x + 7}\]
\[(x - 1)^{2} = (\sqrt{3x + 7})^{2}\]
\[x ^{2} - 2x + 1 = 3x + 7\]
\[x ^{2} - 5x - 6 = 0\]
2. factorise the new equation
\[(x - 6) (x + 1)=0\]
3. there are two possible answers :
x = 6 or x = -1
but x = 1 wouldn't fit the equation. so,
x = 6

Sorry if I was wrong, but the answers fit the equation :)