The equation is given as;
-3 + √ {3x + 7} = x
Take -3 to the right side of the equation
√ {3x + 7} = x+3
Eliminate the square-root on the left side of the equation by squaring both sides
3 x + 7 = {x + 3}^2
Expand the right-hand side
3x + 7 = x^2 + 6x + 9
Collect like terms
0=x^2 +6x -3x +9-7
0= x^2 +3x +2
Re-write the equation as;
x^2 + 3x +2 =0
Factorize to find the value of x
x^2 + x + 2x + 2 = 0
x{x + 1} + 2{ x+ 1} =0
{x+2} {x+ 1} = 0
Solve for x
x+ 2 = 0
x = -2
or
x+ 1 = 0
x = -1
Answer
x = -2 or -1