200x-x^2=30x+6000

Solution for 200x-x^2=30x+6000 equation:

200x-x^2=30x+6000

We move all terms to the left:

200x-x^2-(30x+6000)=0

We add all the numbers together, and all the variables

-1x^2+200x-(30x+6000)=0

We get rid of parentheses

-1x^2+200x-30x-6000=0

We add all the numbers together, and all the variables

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