x*x+x=408

Solution for x*x+x=408 equation:

x*x+x=408

We move all terms to the left:

x*x+x-(408)=0

We add all the numbers together, and all the variables

x+x*x-408=0

Wy multiply elements

x^2+x-408=0

a = 1; b = 1; c = -408;
Δ = b2-4ac
Δ = 12-4·1·(-408)
Δ = 1633
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{1633}}{2*1}=\frac{-1-\sqrt{1633}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1633}}{2*1}=\frac{-1+\sqrt{1633}}{2}
$