4081=x*(260-2x)

Solution for 4081=x*(260-2x) equation:

4081=x(260-2x)

We move all terms to the left:

4081-(x(260-2x))=0

We add all the numbers together, and all the variables

-(x(-2x+260))+4081=0


We calculate terms in parentheses: -(x(-2x+260)), so:

x(-2x+260)

We multiply parentheses

-2x^2+260x

Back to the equation:

-(-2x^2+260x)


We get rid of parentheses

2x^2-260x+4081=0

a = 2; b = -260; c = +4081;
Δ = b2-4ac
Δ = -2602-4·2·4081
Δ = 34952
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:

$\sqrt{\Delta}=\sqrt{34952}=\sqrt{4*8738}=\sqrt{4}*\sqrt{8738}=2\sqrt{8738}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-2\sqrt{8738}}{2*2}=\frac{260-2\sqrt{8738}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+2\sqrt{8738}}{2*2}=\frac{260+2\sqrt{8738}}{4}
$