Question 992036
{{{2x-3=sqrt(30-7x)}}} 



{{{(2x-3)^2=(sqrt(30-7x))^2}}} Square both sides



{{{(2x-3)^2=30-7x}}} Use the rule {{{(sqrt(x))^2 = x}}}



{{{(2x-3)(2x-3)=30-7x}}} Use the rule {{{x^2=x*x}}}



{{{4x^2-12x+9=30-7x}}} FOIL the left side. This is where you made your mistake. You should have {{{4x^2}}} and not {{{4x}}}



{{{4x^2-12x+9-30+7x=0}}} Get everything to one side.



{{{4x^2-5x-21=0}}} Combine like terms.



Next you use the quadratic formula to solve for x. I'll let you finish up.



Note: don't forget to check each possible answer back in the original equation.