81=x^2+x

Solution for 81=x^2+x equation:

81=x^2+x

We move all terms to the left:

81-(x^2+x)=0

We get rid of parentheses

-x^2-x+81=0

We add all the numbers together, and all the variables

-1x^2-1x+81=0

a = -1; b = -1; c = +81;
Δ = b2-4ac
Δ = -12-4·(-1)·81
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{13}}{2*-1}=\frac{1-5\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{13}}{2*-1}=\frac{1+5\sqrt{13}}{-2}
$