An interesting seven variable equation

$6654321a+7554321b+7644321c+7653321d+7654221e+7654311f+7654320g=$ $=7654321(a+b+c+d+e+f+g)-(1000000a+100000b+10000c+1000d+100e+10f+g)=$ $=296754624 \Rightarrow 7654321(a+b+c+d+e+f+g)-296754624=$ $=(1000000a+100000b+10000c+1000d+100e+10f+g) \leftarrow$ this is a 7-digit number $\overline{abcdefg}\geqslant 1111111$ . $7654321 \cdot 38<296754624$ and $7654321 \cdot 41-296754624=17072537$ has more than 7 digits, so $a+b+c+d+e+f+g=39$ and $(a,b,c,d,e,f,g)=(1,7,6,3,8,9,5)$ (because $7654321 \cdot 39-296754624=1763895$ or $a+b+c+d+e+f+g=40$ and $(a,b,c,d,e,f,g)=(9,4,1,8,2,1,6)$ (because $7654321 \cdot 40-296754624=9418216$ . The first option is correct, while the second is contradictory, hence the answer is 39 .

Add a 7-digit number $\overline {abcdefg}$ to both the sides and re-write the given equation as $7654321(a+b+c+d+e+f+g)=296754624+\overline {abcdefg}$ . Simple calculation that gives the next multiple $7654321(1+7+6+3+8+9+5) = 296754624 + 1763895$ . Sum of digits is 39.