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

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

X(X+1)=6(X-1)

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(6(X-1)), so:

6(X-1)

We multiply parentheses

6X-6

Back to the equation:

-(6X-6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2-5X+6=0

a = 1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·1·6
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{-(-5)-1}{2*1}=\frac{4}{2}
=2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*1}=\frac{6}{2}
=3
$