x(64x-x)=60

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

x(64x-x)=60

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(+63x)-60=0

We multiply parentheses

63x^2-60=0

a = 63; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·63·(-60)
Δ = 15120
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:

$\sqrt{\Delta}=\sqrt{15120}=\sqrt{144*105}=\sqrt{144}*\sqrt{105}=12\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{105}}{2*63}=\frac{0-12\sqrt{105}}{126}
=-\frac{12\sqrt{105}}{126}
=-\frac{2\sqrt{105}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{105}}{2*63}=\frac{0+12\sqrt{105}}{126}
=\frac{12\sqrt{105}}{126}
=\frac{2\sqrt{105}}{21}
$