2120=82x+x^2

Solution for 2120=82x+x^2 equation:

2120=82x+x^2

We move all terms to the left:

2120-(82x+x^2)=0

We get rid of parentheses

-x^2-82x+2120=0

We add all the numbers together, and all the variables

-1x^2-82x+2120=0

a = -1; b = -82; c = +2120;
Δ = b2-4ac
Δ = -822-4·(-1)·2120
Δ = 15204
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:

$\sqrt{\Delta}=\sqrt{15204}=\sqrt{4*3801}=\sqrt{4}*\sqrt{3801}=2\sqrt{3801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{3801}}{2*-1}=\frac{82-2\sqrt{3801}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{3801}}{2*-1}=\frac{82+2\sqrt{3801}}{-2}
$