17500=x*(600-x)

Solution for 17500=x*(600-x) equation:

17500=x(600-x)

We move all terms to the left:

17500-(x(600-x))=0

We add all the numbers together, and all the variables

-(x(-1x+600))+17500=0


We calculate terms in parentheses: -(x(-1x+600)), so:

x(-1x+600)

We multiply parentheses

-1x^2+600x

Back to the equation:

-(-1x^2+600x)


We get rid of parentheses

1x^2-600x+17500=0

We add all the numbers together, and all the variables

x^2-600x+17500=0

a = 1; b = -600; c = +17500;
Δ = b2-4ac
Δ = -6002-4·1·17500
Δ = 290000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{290000}=\sqrt{10000*29}=\sqrt{10000}*\sqrt{29}=100\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-100\sqrt{29}}{2*1}=\frac{600-100\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+100\sqrt{29}}{2*1}=\frac{600+100\sqrt{29}}{2}
$