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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+4X^2-4X-8X+8)-((X+1)(2X+1))=0


We calculate terms in parentheses: -((X+1)(2X+1)), so:

(X+1)(2X+1)

We multiply parentheses ..

(+2X^2+X+2X+1)

We get rid of parentheses

2X^2+X+2X+1

We add all the numbers together, and all the variables

2X^2+3X+1

Back to the equation:

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


We get rid of parentheses

4X^2-2X^2-4X-8X-3X+8-1=0

We add all the numbers together, and all the variables

2X^2-15X+7=0

a = 2; b = -15; c = +7;
Δ = b2-4ac
Δ = -152-4·2·7
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-13}{2*2}=\frac{2}{4}
=1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+13}{2*2}=\frac{28}{4}
=7
$