3500=195x-x^2

Solution for 3500=195x-x^2 equation:

3500=195x-x^2

We move all terms to the left:

3500-(195x-x^2)=0

We get rid of parentheses

x^2-195x+3500=0

a = 1; b = -195; c = +3500;
Δ = b2-4ac
Δ = -1952-4·1·3500
Δ = 24025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24025}=155$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-195)-155}{2*1}=\frac{40}{2}
=20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-195)+155}{2*1}=\frac{350}{2}
=175
$