K(x)=7x-x^2

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Solution for K(x)=7x-x^2 equation:



(K)=7K-K^2
We move all terms to the left:
(K)-(7K-K^2)=0
We get rid of parentheses
K^2-7K+K=0
We add all the numbers together, and all the variables
K^2-6K=0
a = 1; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·1·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*1}=\frac{0}{2} =0 $
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*1}=\frac{12}{2} =6 $

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