P(x)=-2x²+20x-42.
P(x)=-2(x²-10x+21)=-2(x²-10x+25-25+21)=
-2[(x-5)²-4]=8-2(x-5)².
P(x)=8-2(x-5)²≥0 to make a profit; 8≥2(x-5)², 4≥(x-5)², 2≥|x-5|.
So x-5≤2, x≤7; or 5-x≤2, 3≤x, x≥3.
If the company sells 5000 pairs of shoes (x=5) it maximises profit. If it sells 3000 it breaks even (no profit); if it sells 7000 it breaks even. So to break even the company has to sell 3000 pairs of shoes.