520=2.205x+0.0517x^2

Solution for 520=2.205x+0.0517x^2 equation:

520=2.205x+0.0517x^2

We move all terms to the left:

520-(2.205x+0.0517x^2)=0

We get rid of parentheses

-0.0517x^2-2.205x+520=0

a = -0.0517; b = -2.205; c = +520;
Δ = b2-4ac
Δ = -2.2052-4·(-0.0517)·520
Δ = 112.398025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.205)-\sqrt{112.398025}}{2*-0.0517}=\frac{2.205-\sqrt{112.398025}}{-0.1034}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.205)+\sqrt{112.398025}}{2*-0.0517}=\frac{2.205+\sqrt{112.398025}}{-0.1034}
$