X*(x-1)-x=35

Solution for X*(x-1)-x=35 equation:

X(X-1)-X=35

We move all terms to the left:

X(X-1)-X-(35)=0

We add all the numbers together, and all the variables

-1X+X(X-1)-35=0

We multiply parentheses

X^2-1X-1X-35=0

We add all the numbers together, and all the variables

X^2-2X-35=0

a = 1; b = -2; c = -35;
Δ = b2-4ac
Δ = -22-4·1·(-35)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*1}=\frac{14}{2}
=7
$