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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

2(X+4)

We multiply parentheses

2X+8

Back to the equation:

-(2X+8)


We get rid of parentheses

X^2-1X-2X-2X+2-8=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 = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*1}=\frac{12}{2}
=6
$