Solve $x^2/3+x/2-1=0$. Give the roots in surd form.

Multiply through by 6: $2x^2+3x-6=0$, so $a=2,b=3,c=-6.x=\frac{-3\pm \sqrt{9+48}}{4}=\frac{-3\pm \sqrt{57}}{4}$. Since $c$ is negative, $-4ac$ is +48 — computing 9 − 48 instead is what makes a student wrongly report "no real roots".