Question 992036
First step: Square both sides:
(2x-3)^2 
.
FOIL:Multiply first terms: 
{{{2x*2x=4x^2}}} {{{not}}} {{{4x}}}
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Continued:
{{{2x-3=sqrt(30-7x)}}}
{{{(2x-3)^2=30-7x}}}
{{{4x^2-12x+9=30-7x}}}
{{{4x^2-5x-21=0}}}
{{{(4x+7)(x-3)=0}}}
{{{4x+7=0}}} {{{OR}}} {{{x-3=0}}}
{{{4x=-7}}} {{{OR}}} {{{x=3}}}
{{{x=-7/4}}} {{{OR}}} {{{x=3}}}
The domain of the original is:
{{{3/2}}}<{{{x}}}<{{{30/7}}}
so -7/4  is eliminated, leaving:
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ANSWER:x=3