Solve $x(x-2)=3x+24$ using the quadratic formula.

$x^2-2x=3x+24$ gives $x^2-5x-24=0.x=\frac{5\pm \sqrt{25+96}}{2}=\frac{5\pm 11}{2}=8$ or −3. Check: $8(8-2)=48=3(8)+24$, and $(-3)(-3-2)=15=3(-3)+24$. Reading $x(x-2)=0$ gives the wrong pair 0 and 2 — a product may be split like that only when it equals 0. Carrying +24 across without changing its sign gives $x^2+x+24=0$, whose discriminant 1 − 96 is negative.