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x(x-1)/2=66
We move all terms to the left:
x(x-1)/2-(66)=0
We multiply all the terms by the denominator
x(x-1)-66*2=0
We add all the numbers together, and all the variables
x(x-1)-132=0
We multiply parentheses
x^2-1x-132=0
a = 1; b = -1; c = -132;
Δ = b2-4ac
Δ = -12-4·1·(-132)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-23}{2*1}=\frac{-22}{2} =-11 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+23}{2*1}=\frac{24}{2} =12 $
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