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-k+-k(k+1)=2k
We move all terms to the left:
-k+-k(k+1)-(2k)=0
We add all the numbers together, and all the variables
-3k-k(k+1)=0
We multiply parentheses
-k^2-3k-k=0
We add all the numbers together, and all the variables
-1k^2-4k=0
a = -1; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-1)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{16}=4$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-1}=\frac{0}{-2} =0 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-1}=\frac{8}{-2} =-4 $
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