Question 146622
First step is always get rid of the denominators. 
16 seems to be the largest common denominator.
Multiply both sides by 16. 
{{{x^2+(5/2)x+25/16=11/8}}}
{{{16x^2+40x+25=22}}}
{{{16x^2+40x+3=0}}}
Time to break out the quadratic formula,
{{{x[1,2]=(-b+-sqrt(b^2-4ac))/2a}}}
{{{x[1,2]=(-40+-sqrt(40^2-4(16)3))/2(16)}}}
{{{x[1,2]=(-40+-sqrt(1600-192))/32}}}
{{{x[1,2]=(-40+-sqrt(1408))/32}}}
{{{x[1,2]=(-40+-37.52)/32}}}
{{{x[1,2]=(-40+-37.52)/32}}}
{{{x[1]=(-2.48)/32}}}
{{{x[1]=-0.078}}}
{{{x[2]=(-77.52)/32}}}
{{{x[2]=2.42}}}