81=3x+x^2

Solution for 81=3x+x^2 equation:

81=3x+x^2

We move all terms to the left:

81-(3x+x^2)=0

We get rid of parentheses

-x^2-3x+81=0

We add all the numbers together, and all the variables

-1x^2-3x+81=0

a = -1; b = -3; c = +81;
Δ = b2-4ac
Δ = -32-4·(-1)·81
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{37}}{2*-1}=\frac{3-3\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{37}}{2*-1}=\frac{3+3\sqrt{37}}{-2}
$