Question 685853
Square both sides to get 


7x - 8 = 3x + 12


Now solve for x


{{{7x-8=3x+12}}} Start with the given equation.



{{{7x=3x+12+8}}} Add {{{8}}} to both sides.



{{{7x-3x=12+8}}} Subtract {{{3x}}} from both sides.



{{{4x=12+8}}} Combine like terms on the left side.



{{{4x=20}}} Combine like terms on the right side.



{{{x=(20)/(4)}}} Divide both sides by {{{4}}} to isolate {{{x}}}.



{{{x=5}}} Reduce.



So the *possible* solution is {{{x=5}}} 


You need to check if it's actually the solution. You do so by plugging it back in like this


{{{sqrt(7x-8) = sqrt(3x+12)}}}


{{{sqrt(7(5)-8) = sqrt(3(5)+12)}}}


{{{sqrt(35-8) = sqrt(15+12)}}}


{{{sqrt(27) = sqrt(27)}}} which is TRUE


So {{{x=5}}} is indeed the solution.