x²=37²-(47-x)²
x²=(37-(47-x))(37+(47-x))
x²=(37-47+x)(37+47-x)
x²=(-10+x)(84-x)
x²=-840+84x+10x-x²
2x²-94x+840=0
x²-47x+420=0
D=(-47)²-4*1*420=2209-1680=529=23²
x₁=(47+23)/2=35
x₂=(47-23)/2=12
или так:
x²=37²-(47-x)²
x²=1369-(2209-94x+x²)
x²=1369-2209+94x-x²
2x-94x+840=0
x²-47x+420=0
D=(-47)²-4*1*420=2209-1680=529=23²
x₁=(47+23)/2=35
x₂=(47-23)/2=12