Question 657890
If I'm reading the problem statement correctly, we are to find x such that
{{{sqrt(5x - 4) = x - 2}}}
Squaring both sides:
{{{5x - 4 = x^2 - 4x + 4}}}
{{{x^2 - 4x + 4 - (5x - 4) = 0}}}
{{{x^2 -9x + 8}}}
We can solve for x using the quadratic equation {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} with a=1, b=-9, and c=8:
{{{x = (-(-9) +- sqrt( (-9)^2-4*1*8 ))/(2*1) }}}
{{{x = (9 +- sqrt( 81-32 ))/2 }}}
{{{x = (9 +- sqrt( 49 ))/2 }}}
{{{x = (9 +- 7)/2 }}}
So x = 1 or x = 8.  However x cannot be 1 because we are told that the principle root of 5x-4 = x-2, but x-2 = -1, so we would not be taking the principle root.

Hence, x = 8.