X(x-1)=-2(x-4)-2

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

X(X-1)=-2(X-4)-2

We move all terms to the left:

X(X-1)-(-2(X-4)-2)=0

We multiply parentheses

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


We calculate terms in parentheses: -(-2(X-4)-2), so:

-2(X-4)-2

We multiply parentheses

-2X+8-2

We add all the numbers together, and all the variables

-2X+6

Back to the equation:

-(-2X+6)


We get rid of parentheses

X^2-1X+2X-6=0

We add all the numbers together, and all the variables

X^2+X-6=0

a = 1; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·1·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*1}=\frac{4}{2}
=2
$