x(6+x)-2(x+1)-5x=4-2,0

Solution for x(6+x)-2(x+1)-5x=4-2,0 equation:

x(6+x)-2(x+1)-5x=4-2.0

We move all terms to the left:

x(6+x)-2(x+1)-5x-(4-2.0)=0

We add all the numbers together, and all the variables

x(x+6)-2(x+1)-5x-2=0

We add all the numbers together, and all the variables

-5x+x(x+6)-2(x+1)-2=0

We multiply parentheses

x^2-5x+6x-2x-2-2=0

We add all the numbers together, and all the variables

x^2-1x-4=0

a = 1; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·1·(-4)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{17}}{2*1}=\frac{1-\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*1}=\frac{1+\sqrt{17}}{2}
$