12x*5x=1

Solution for 12x*5x=1 equation:

12x*5x=1

We move all terms to the left:

12x*5x-(1)=0

Wy multiply elements

60x^2-1=0

a = 60; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·60·(-1)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*60}=\frac{0-4\sqrt{15}}{120}
=-\frac{4\sqrt{15}}{120}
=-\frac{\sqrt{15}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*60}=\frac{0+4\sqrt{15}}{120}
=\frac{4\sqrt{15}}{120}
=\frac{\sqrt{15}}{30}
$