x+x*x=272

Solution for x+x*x=272 equation:

x+x*x=272

We move all terms to the left:

x+x*x-(272)=0

Wy multiply elements

x^2+x-272=0

a = 1; b = 1; c = -272;
Δ = b2-4ac
Δ = 12-4·1·(-272)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-33}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+33}{2*1}=\frac{32}{2}
=16
$