x+(x+1)(x+2)=42

Solution for x+(x+1)(x+2)=42 equation:

x+(x+1)(x+2)=42

We move all terms to the left:

x+(x+1)(x+2)-(42)=0

We multiply parentheses ..

(+x^2+2x+x+2)+x-42=0

We get rid of parentheses

x^2+2x+x+x+2-42=0

We add all the numbers together, and all the variables

x^2+4x-40=0

a = 1; b = 4; c = -40;
Δ = b2-4ac
Δ = 42-4·1·(-40)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{11}}{2*1}=\frac{-4-4\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{11}}{2*1}=\frac{-4+4\sqrt{11}}{2}
$