K(x)=9-x2

Solution for K(x)=9-x2 equation:

(K)=9-K2

We move all terms to the left:

(K)-(9-K2)=0

We add all the numbers together, and all the variables

-(-1K^2+9)+K=0

We get rid of parentheses

1K^2+K-9=0

We add all the numbers together, and all the variables

K^2+K-9=0

a = 1; b = 1; c = -9;
Δ = b2-4ac
Δ = 12-4·1·(-9)
Δ = 37
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{37}}{2*1}=\frac{-1-\sqrt{37}}{2}
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*1}=\frac{-1+\sqrt{37}}{2}
$