Question 1152545
.
<pre>

Introduce new variable  y = {{{sqrt(x)}}}.


Then your equation takes the form


    4y^2 - 11y + 6 = 0.


Solve this quadratic equation using the quadrtic formula


    {{{y[1,2]}}} = {{{(11 +- sqrt((-11)^2 - 4*4*6))/(2*4)}}} = {{{(11 +- sqrt(25))/8}}} = {{{(11 +- 5)/8}}}.



Case 1.  {{{y[1]}}} = {{{(11+5)/8}}} = {{{16/8}}} = 2.


         Then  {{{sqrt(x)}}} = 2;  hence,  x = 4.



Case 2.  {{{y[2]}}} = {{{(11-5)/8}}} = {{{6/8}}} = {{{3/4}}}.


         Then  {{{sqrt(x)}}} = {{{3/4}}};  hence,  x = {{{9/16}}}.


<U>ANSWER</U>.  The given equation has two and only two solutions:  x= 4  and  x= {{{9/16}}}.
</pre>


Solved, answered and explained in most detailed way, as requested.   And completed.


--------------


Introducing new variable is a standard way of solving such equations.