J(x)=x2-x

Solution for J(x)=x2-x equation:

(J)=J2-J

We move all terms to the left:

(J)-(J2-J)=0

We add all the numbers together, and all the variables

-(+J^2-1J)+J=0

We get rid of parentheses

-J^2+1J+J=0

We add all the numbers together, and all the variables

-1J^2+2J=0

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

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