Question 297318
You can graph it. 
{{{ graph( 300, 300, -10, 10, -10, 10,  x^2+3x-6) }}} 
Since it crosses the x-axis the solutions are real. 
Now use the quadratic formula,
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-3 +- sqrt( 3^2-4*1*(-6) ))/(2*1) }}}
{{{x = (-3 +- sqrt( 9+25 ))/(2) }}}
{{{x = (-3 +- sqrt( 34))/(2) }}}
Since 34 is not a perfect square, the solutions are irrational.