x(33-x)=260

Solution for x(33-x)=260 equation:

x(33-x)=260

We move all terms to the left:

x(33-x)-(260)=0

We add all the numbers together, and all the variables

x(-1x+33)-260=0

We multiply parentheses

-1x^2+33x-260=0

a = -1; b = 33; c = -260;
Δ = b2-4ac
Δ = 332-4·(-1)·(-260)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-7}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+7}{2*-1}=\frac{-26}{-2}
=+13
$