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k(k+1)=235.2
We move all terms to the left:
k(k+1)-(235.2)=0
We add all the numbers together, and all the variables
k(k+1)-235.2=0
We multiply parentheses
k^2+k-235.2=0
a = 1; b = 1; c = -235.2;
Δ = b2-4ac
Δ = 12-4·1·(-235.2)
Δ = 941.8
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{941.8}}{2*1}=\frac{-1-\sqrt{941.8}}{2} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{941.8}}{2*1}=\frac{-1+\sqrt{941.8}}{2} $
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