Field sowing days

Farmers had to sow 200 hectares of fields. They reduced the planned sowing time by two days while planting 5 hectares more each day than intended. How many days did the sowing last?

Final Answer:

x =  8

Step-by-step explanation:

$$\begin{gathered} 200ha=x\cdot y=(x+2)\cdot (y-5) \\ 200=x\cdot y \\ 200=x\cdot y+2y-5x-10 \\ 2y-5x-10-0 \\ 2\cdot 200/x-5x-10=0 \\ 400-5\cdot x^2-10x=0 \\ 400-5\cdot x^2-10x=0 \\ -5x^2-10x+400=0 \\ 5x^2+10x-400=0 \\ 5...\text{ prime number} \\ 10=2\cdot 5 \\ 400=2^4\cdot 5^2 \\ \text{GCD}(5,10,400)=5 \\ {x}^2+2x-80=0 \\ a=1;b=2;c=-80 \\ D=b^2-4ac=2^2-4\cdot 1\cdot (-80)=324 \\ D>0 \\ {x}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{-2\pm \sqrt{324}}{2} \\ {x}_{1,2}=\frac{-2\pm 18}{2} \\ {x}_{1,2}=-1\pm 9 \\ {x}_1=8 \\ {x}_2=-10 \\ x=x_1=8 \\ y=200/x=200/8=25 \\ \text{ Verifying Solution: } \\ {s}_1=x\cdot y=8\cdot 25=200\text{ha} \\ {s}_2=(x+2)\cdot (y-5)=(8+2)\cdot (25-5)=200\text{ha} \end{gathered}$$

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