272=x^2+x

Solution for 272=x^2+x equation:

272=x^2+x

We move all terms to the left:

272-(x^2+x)=0

We get rid of parentheses

-x^2-x+272=0

We add all the numbers together, and all the variables

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