[tex] \frac{2x+3}{x+2} = \frac{x-1}{x-2}
[/tex]
(2x+3)(x-2)=(x+2)(x-1)
2x²-4x+3x-6=x²-x+2x-2
2x²-x²-4x+3x+x-2x=-2+6
x²-2x=4
x²-2x-4=0
a=1 b=-2 c=-4
Δ=b²-4ac
Δ=(-2)²+16
Δ=4+16
Δ=20
x₁=[tex] \frac{-b- \sqrt{delta} }{2a}= \frac{2- \sqrt{20} }{2}= \frac{2- 2\sqrt{5} }{2} = 2- \sqrt{5} [/tex]
x₂=[tex] \frac{-b+ \sqrt{delta} }{2a}= \frac{2+ \sqrt{20} }{2} = \frac{2+2 \sqrt{5} }{2} =2+ \sqrt{5} [/tex]
S={2-√5, 2+√5}
