X(x-1)=6(x-2)

Solution for X(x-1)=6(x-2) equation:

X(X-1)=6(X-2)

We move all terms to the left:

X(X-1)-(6(X-2))=0

We multiply parentheses

X^2-1X-(6(X-2))=0


We calculate terms in parentheses: -(6(X-2)), so:

6(X-2)

We multiply parentheses

6X-12

Back to the equation:

-(6X-12)


We get rid of parentheses

X^2-1X-6X+12=0

We add all the numbers together, and all the variables

X^2-7X+12=0

a = 1; b = -7; c = +12;
Δ = b2-4ac
Δ = -72-4·1·12
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{-(-7)-1}{2*1}=\frac{6}{2}
=3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*1}=\frac{8}{2}
=4
$