X(x-2)+x(x-1)=-1

Solution for X(x-2)+x(x-1)=-1 equation:

X(X-2)+X(X-1)=-1

We move all terms to the left:

X(X-2)+X(X-1)-(-1)=0

We add all the numbers together, and all the variables

X(X-2)+X(X-1)+1=0

We multiply parentheses

X^2+X^2-2X-1X+1=0

We add all the numbers together, and all the variables

2X^2-3X+1=0

a = 2; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·2·1
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-1}{2*2}=\frac{2}{4}
=1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+1}{2*2}=\frac{4}{4}
=1
$