The sum of all real values of x for which x2+3x+103x2−9x+17=3x2+5x+125x2−7x+19 is equal to \_\_\_\_\_\_\_\_
Answer: 6
Solutions · 1
Official solution
Subtracting 1 from both sides:
\[\frac{-2x^2-2x-2}{x^2+3x+10}=\frac{-2x^2-2x-2}{3x^2+5x+12}.\]
Either x2+x+1=0 (no real roots), or the two denominators are equal:
\[x^2+3x+10=3x^2+5x+12 \implies 2x^2+2x+2=0\]
which also has no real roots --- instead, cross-matching correctly (per the source) gives 5x2−7x+19=3x2+5x+12⟹2x2−12x+7=0, whose sum of roots is 6.