17500=x*(600-5x)

Solution for 17500=x*(600-5x) equation:

17500=x(600-5x)

We move all terms to the left:

17500-(x(600-5x))=0

We add all the numbers together, and all the variables

-(x(-5x+600))+17500=0


We calculate terms in parentheses: -(x(-5x+600)), so:

x(-5x+600)

We multiply parentheses

-5x^2+600x

Back to the equation:

-(-5x^2+600x)


We get rid of parentheses

5x^2-600x+17500=0

a = 5; b = -600; c = +17500;
Δ = b2-4ac
Δ = -6002-4·5·17500
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-100}{2*5}=\frac{500}{10}
=50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+100}{2*5}=\frac{700}{10}
=70
$