x(x-2)(x+2)=60x

Solution for x(x-2)(x+2)=60x equation:

x(x-2)(x+2)=60x

We move all terms to the left:

x(x-2)(x+2)-(60x)=0

We add all the numbers together, and all the variables

-60x+x(x-2)(x+2)=0

We use the square of the difference formula

x^2-60x-4=0

a = 1; b = -60; c = -4;
Δ = b2-4ac
Δ = -602-4·1·(-4)
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{226}}{2*1}=\frac{60-4\sqrt{226}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{226}}{2*1}=\frac{60+4\sqrt{226}}{2}
$