(140x-x^2-2000)=0

Solution for (140x-x^2-2000)=0 equation:

(140x-x^2-2000)=0

We get rid of parentheses

-x^2+140x-2000=0

We add all the numbers together, and all the variables

-1x^2+140x-2000=0

a = -1; b = 140; c = -2000;
Δ = b2-4ac
Δ = 1402-4·(-1)·(-2000)
Δ = 11600
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:

$\sqrt{\Delta}=\sqrt{11600}=\sqrt{400*29}=\sqrt{400}*\sqrt{29}=20\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-20\sqrt{29}}{2*-1}=\frac{-140-20\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+20\sqrt{29}}{2*-1}=\frac{-140+20\sqrt{29}}{-2}
$