x(850-x)=1700

Solution for x(850-x)=1700 equation:

x(850-x)=1700

We move all terms to the left:

x(850-x)-(1700)=0

We add all the numbers together, and all the variables

x(-1x+850)-1700=0

We multiply parentheses

-1x^2+850x-1700=0

a = -1; b = 850; c = -1700;
Δ = b2-4ac
Δ = 8502-4·(-1)·(-1700)
Δ = 715700
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:

$\sqrt{\Delta}=\sqrt{715700}=\sqrt{100*7157}=\sqrt{100}*\sqrt{7157}=10\sqrt{7157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(850)-10\sqrt{7157}}{2*-1}=\frac{-850-10\sqrt{7157}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(850)+10\sqrt{7157}}{2*-1}=\frac{-850+10\sqrt{7157}}{-2}
$