K(x)=2x^2-x

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

(K)=2K^2-K

We move all terms to the left:

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

We get rid of parentheses

-2K^2+K+K=0

We add all the numbers together, and all the variables

-2K^2+2K=0

a = -2; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-2)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-2}=\frac{-4}{-4}
=1
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-2}=\frac{0}{-4}
=0
$