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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


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

-x(x+6)

We multiply parentheses

-x^2-6x

We add all the numbers together, and all the variables

-1x^2-6x

Back to the equation:

-(-1x^2-6x)


We add all the numbers together, and all the variables

-(-1x^2-6x)-2x-3=0

We get rid of parentheses

1x^2+6x-2x-3=0

We add all the numbers together, and all the variables

x^2+4x-3=0

a = 1; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·1·(-3)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{7}}{2*1}=\frac{-4-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{7}}{2*1}=\frac{-4+2\sqrt{7}}{2}
$