Question 155290
{{{sqrt(5x+1)=x-4}}}
then
{{{5x+1=(x-4)^2}}}
then
{{{5x+1=x^2-8x+16}}}
then
{{{-x^2+13x-15=0}}}
then
{{{x = (-13 +- sqrt( 13^2-4*(-1)*(-15) ))/(2*(-1)) }}}
then
{{{x = (-13 +- sqrt( 13^2-4*(-1)*(-15) ))/(2*(-1)) }}}
then
{{{x = (-13 +- sqrt(109))/(-2) }}}
x=11.72 (aprox) or x=1.28 (aprox)

Checking:
x-4 is positive if x=11.72 but is negative if x=1.28
{{{sqrt(5x+1)}}} is always positive so x=1.28 is a extraneous solution
and the only solution for the first equation is the first

Answer:{{{x = (-13 - sqrt(109))/(-2) }}}