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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(2X+2)(X-4)

We multiply parentheses ..

(+2X^2-8X+2X-8)

We get rid of parentheses

2X^2-8X+2X-8

We add all the numbers together, and all the variables

2X^2-6X-8

Back to the equation:

-(2X^2-6X-8)


We get rid of parentheses

X^2-2X^2-4X+X+6X-4+8=0

We add all the numbers together, and all the variables

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

a = -1; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-1)·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*-1}=\frac{-8}{-2}
=+4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*-1}=\frac{2}{-2}
=-1
$