6(x+1)=2(x+1)*x

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

6(x+1)=2(x+1)*x

We move all terms to the left:

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

We multiply parentheses

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


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

2(x+1)*x

We multiply parentheses

2x^2+2x

Back to the equation:

-(2x^2+2x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 4; c = +6;
Δ = b2-4ac
Δ = 42-4·(-2)·6
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-2}=\frac{4}{-4}
=-1
$