(2x-1)(x+1)=4(1+x)(1-x)-6x

Solution for (2x-1)(x+1)=4(1+x)(1-x)-6x equation:

(2x-1)(x+1)=4(1+x)(1-x)-6x

We move all terms to the left:

(2x-1)(x+1)-(4(1+x)(1-x)-6x)=0

We add all the numbers together, and all the variables

(2x-1)(x+1)-(4(x+1)(-1x+1)-6x)=0

We multiply parentheses ..

(+2x^2+2x-1x-1)-(4(x+1)(-1x+1)-6x)=0


We calculate terms in parentheses: -(4(x+1)(-1x+1)-6x), so:

4(x+1)(-1x+1)-6x

We add all the numbers together, and all the variables

-6x+4(x+1)(-1x+1)

We multiply parentheses ..

4(-1x^2+x-1x+1)-6x

We multiply parentheses

-4x^2+4x-4x-6x+4

We add all the numbers together, and all the variables

-4x^2-6x+4

Back to the equation:

-(-4x^2-6x+4)


We get rid of parentheses

2x^2+4x^2+2x-1x+6x-1-4=0

We add all the numbers together, and all the variables

6x^2+7x-5=0

a = 6; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·6·(-5)
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{-(7)-13}{2*6}=\frac{-20}{12}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*6}=\frac{6}{12}
=1/2
$