x+(x+1)(x+2)=168

Solution for x+(x+1)(x+2)=168 equation:

x+(x+1)(x+2)=168

We move all terms to the left:

x+(x+1)(x+2)-(168)=0

We multiply parentheses ..

(+x^2+2x+x+2)+x-168=0

We get rid of parentheses

x^2+2x+x+x+2-168=0

We add all the numbers together, and all the variables

x^2+4x-166=0

a = 1; b = 4; c = -166;
Δ = b2-4ac
Δ = 42-4·1·(-166)
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{170}}{2*1}=\frac{-4-2\sqrt{170}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{170}}{2*1}=\frac{-4+2\sqrt{170}}{2}
$