K(x)=4x^2-1

Solution for K(x)=4x^2-1 equation:

(K)=4K^2-1

We move all terms to the left:

(K)-(4K^2-1)=0

We get rid of parentheses

-4K^2+K+1=0

a = -4; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-4)·1
Δ = 17
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{17}}{2*-4}=\frac{-1-\sqrt{17}}{-8}
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*-4}=\frac{-1+\sqrt{17}}{-8}
$