\require{AMSmath}

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Los op:

  1. 6x²+5x-6=0
  2. 2x²-3x=2
  3. 2x²=9x+5

Uitwerking

  1. 6x²+5x-6=0
    6·-6=-36
    -4+9=5
    -4·9=-36
    6x²+5x-6=0
    6x²-4x+9x-6=0
    2x(3x-2)+3(3x-2)=0
    (2x+3)(3x+2)=0
    2x+3=0 of 3x+2=0
    2x=-3 of 3x=-2
    x= $-1\frac{1}{2}$ of x= $-\frac{2}{3}$
  2. 2x²-3x=2
    2x²-3x-2=0
    2·-2=-4
    -4·1=-4
    -4+1=-3
    2x²-4x+x-2=0
    2x(x-2)+x-2=0
    (2x+1)(x-2)=0
    2x+1=0 of x-2=0
    2x=-1 of x=2
    x= $-\frac{1}{2}$ of x=2
  3. 2x²=9x+5
    2x²-9x-5=0
    2·-5=-10
    -10·1=-10
    -10+1=-9
    2x²-10x+x-5=0
    2x(x-5)+(x-5)=0
    (2x+1)(x-5)=0
    2x+1=0 of x-5=0
    2x=-1 of x=5
    x= $-\frac{1}{2}$ of x=5

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