Question 729072
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square root of x+7=square root of 2x-3    (+2) not under the square root)
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I don't know what "X=507+338√2 ≈985.0042 from @lynnlo(4176) is all about.

square root of x+7=square root of 2x-3    (+2) not under the square root)
              {{{sqrt(x + 7) = sqrt(2x - 3) + 2}}}
            {{{(sqrt(x + 7))^2 = (sqrt(2x - 3) + 2)^2}}} --- Squaring both sides
                {{{x + 7 = 2x - 3 + 4sqrt(2x - 3) + 4}}} 
                {{{x + 7 = 2x + 4sqrt(2x - 3) + 1}}}
         {{{x + 7 - 2x - 1 = 4sqrt(2x - 3)}}}
              {{{- x + 6 = 4sqrt(2x - 3)}}}
            {{{(- x + 6)^2 = (4sqrt(2x - 3))^2}}} ----- Squaring both sides
         {{{x^2 - 12x + 36 = 16(2x - 3)}}}
         {{{x^2 - 12x + 36 = 32x - 48}}}
{{{x^2 - 12x + 36 - 32x + 48 = 0}}}
         {{{x^2 - 44x + 84 = 0}}}
     (x - 42)(x - 2) = 0
      x - 42 = 0      OR     x - 2 = 0
           x = 42     OR         x = 2

However, x = 42 is an EXTRANEOUS solution, so ONLY solution is: <font color = red><font size = 4><b>x = 2</font></font></b></pre>