x+(x+1)(x+2)+x=366

Solution for x+(x+1)(x+2)+x=366 equation:

x+(x+1)(x+2)+x=366

We move all terms to the left:

x+(x+1)(x+2)+x-(366)=0

We add all the numbers together, and all the variables

2x+(x+1)(x+2)-366=0

We multiply parentheses ..

(+x^2+2x+x+2)+2x-366=0

We get rid of parentheses

x^2+2x+x+2x+2-366=0

We add all the numbers together, and all the variables

x^2+5x-364=0

a = 1; b = 5; c = -364;
Δ = b2-4ac
Δ = 52-4·1·(-364)
Δ = 1481
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{-(5)-\sqrt{1481}}{2*1}=\frac{-5-\sqrt{1481}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1481}}{2*1}=\frac{-5+\sqrt{1481}}{2}
$