0=-x^2+170x-6000

Solution for 0=-x^2+170x-6000 equation:

0=-x^2+170x-6000

We move all terms to the left:

0-(-x^2+170x-6000)=0

We add all the numbers together, and all the variables

-(-x^2+170x-6000)=0

We get rid of parentheses

x^2-170x+6000=0

a = 1; b = -170; c = +6000;
Δ = b2-4ac
Δ = -1702-4·1·6000
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-70}{2*1}=\frac{100}{2}
=50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+70}{2*1}=\frac{240}{2}
=120
$