Question 906478
{{{3sqrt(5x-6)= 13-2sqrt(7-x)}}}
{{{9(5x-6)=169-52sqrt(7-x)+4(7-x)}}}
{{{45x-54=169-52sqrt(7-x)+28-4x}}}
{{{45x-54=-4x+197-52sqrt(7-x)}}}
{{{49x-251=-52sqrt(7-x)}}}
{{{2401x^2-24598x+63001=2704(7-x)}}}
{{{2401x^2-24598x+63001=18928-2704x}}}
{{{2401x^2-21894x+44073=0}}}
{{{(x-3)(2401x-14691)=0}}}
Two solutions:
{{{x-3=0}}}
{{{x=3}}}
and
{{{2401x-14691=0}}}
{{{2401x=14691}}}
{{{x=14691/2401}}}
Verify both solutions.
{{{3*sqrt(5(3)-6)+2sqrt(7-3)=13}}}
{{{3*sqrt(9)+2sqrt(4)=13}}}
{{{3*3+2*2=13}}}
{{{9+4=13}}}
{{{13=13}}}
Good solution.
{{{3*sqrt(73455/2401-6)+2*sqrt(7-14691/2401)=13}}}
{{{3*sqrt(59049/2401)+2*sqrt(2116/2401)=13}}}
{{{3*(243/49)+2*(46/49)=13}}}
{{{(729/49)+(92/49)=13}}}

{{{821/49=13}}}
{{{16&37/49=13}}}
False, this is not a solution.
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{{{highlight(x=3)}}}