x(64-x)=60

Solution for x(64-x)=60 equation:

x(64-x)=60

We move all terms to the left:

x(64-x)-(60)=0

We add all the numbers together, and all the variables

x(-1x+64)-60=0

We multiply parentheses

-1x^2+64x-60=0

a = -1; b = 64; c = -60;
Δ = b2-4ac
Δ = 642-4·(-1)·(-60)
Δ = 3856
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:

$\sqrt{\Delta}=\sqrt{3856}=\sqrt{16*241}=\sqrt{16}*\sqrt{241}=4\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{241}}{2*-1}=\frac{-64-4\sqrt{241}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{241}}{2*-1}=\frac{-64+4\sqrt{241}}{-2}
$