Question 991000
{{{sqrt(4x+1)-sqrt(x-1)=2}}}


{{{sqrt(4x+1)=sqrt(x-1)+2}}}
{{{4x+1=x-1+4sqrt(x-1)+4}}}
{{{4x-x+1+1-4=4sqrt(x-1)}}}
{{{3x-4=4sqrt(x-1)}}}
{{{9x^2-24x+16=16(x-1)}}}
{{{9x^2-24x+16-16x+16=0}}}
{{{9x^2-40x+32=0}}}


{{{x=(40+- sqrt(1600-4*9(32)))/(2*9)}}}


{{{x=(40+- sqrt(448))/(2*9)}}}


{{{x=(40+- sqrt(16*28))/(2*9)}}}


{{{x=40/2+- (4/2)(1/9)sqrt(28)}}}


{{{x=20+- (2/9)sqrt(28)}}}


{{{highlight(x=20+- (4/9)sqrt(7))}}}


Check the minus-form carefully.
{{{x=20-(4/9)2.646}}}
{{{x=18.824}}}, approximation.  This will work, as well as the plus-form.