we have that
6x^2 +12x+5=0
to find the x intercepts resolve the second order equation
x=[-b(+-)√(b²-4ac)]/2a
x1=[-12(+)√(12²-4*6*5)]/12---> [-12(+)√(144-120)]/12
=[-12(+)√(24)]/12--------> -1+√24/12-----> -1+√6/6
x1=-1+√6/6
so
x2=-1-√6/6
see the graph in the attached figure
the answer is
the x-intercepts for the graph of the quadratic function in exact form are
x1=-1+√6/6
x2=-1-√6/6
