(X-2)(x+1)=3(x+1)

Solution for (X-2)(x+1)=3(x+1) equation:

(X-2)(X+1)=3(X+1)

We move all terms to the left:

(X-2)(X+1)-(3(X+1))=0

We multiply parentheses ..

(+X^2+X-2X-2)-(3(X+1))=0


We calculate terms in parentheses: -(3(X+1)), so:

3(X+1)

We multiply parentheses

3X+3

Back to the equation:

-(3X+3)


We get rid of parentheses

X^2+X-2X-3X-2-3=0

We add all the numbers together, and all the variables

X^2-4X-5=0

a = 1; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·1·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*1}=\frac{10}{2}
=5
$