\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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