A quadratic equation can have no real solution
a[tex]a x^{2} +bx+c=0[/tex]
If [tex] b^{2} -4ac\ \textless \ 0[/tex] then the equation has no real solutions
Even simultaneous equations can have no solutions
[tex]ax+by=c------1[/tex]
[tex]ax+by=d------2[/tex]
I these two equations the two expressions equal different things, so the equation has no solutions