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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

x(-1x+1)

We multiply parentheses

-1x^2+x

Back to the equation:

-(-1x^2+x)


We get rid of parentheses

1x^2-x+6x+6=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 = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*1}=\frac{-4}{2}
=-2
$