x²-4x=6 (mutam 6 in partea stanga cu semn schimbat)
x²-4x-6=0
avem o ecuatie de gradul II
a=1
b=-4
c=-6
calculam Δ(delta)
Δ=b²-4ac
=(-4)²- 4·1·(-6)
=16-(-24)
=16+24
=40
Δ>0 ⇒ ecuatia are 2 solutii reale distincte
[tex]x_{1} = \frac{-b+ \sqrt{delta} }{2a}= \frac{-(-4)+ \sqrt{40} }{2*1}= \frac{2*2+2 \sqrt{10} }{2} = \frac{2*(2+ \sqrt{10}) }{2}= 2+ \sqrt{10} [/tex]
[tex]x_2 = \frac{-b- \sqrt{delta} }{2a} = \frac{-(-4)- \sqrt{40} }{2*1} = \frac{2*2-2 \sqrt{10} }{2} =\frac{2*(2- \sqrt{10)} }{2}=2-\sqrt{10} [/tex]
S={2+√10 ; 2-√10}
