x=220+3.3x-0.06x^2

Solution for x=220+3.3x-0.06x^2 equation:

x=220+3.3x-0.06x^2

We move all terms to the left:

x-(220+3.3x-0.06x^2)=0

We get rid of parentheses

0.06x^2-3.3x+x-220=0

We add all the numbers together, and all the variables

0.06x^2-2.3x-220=0

a = 0.06; b = -2.3; c = -220;
Δ = b2-4ac
Δ = -2.32-4·0.06·(-220)
Δ = 58.09
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{-(-2.3)-\sqrt{58.09}}{2*0.06}=\frac{2.3-\sqrt{58.09}}{0.12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.3)+\sqrt{58.09}}{2*0.06}=\frac{2.3+\sqrt{58.09}}{0.12}
$