36(x)^2/120=1

Solution for 36(x)^2/120=1 equation:

36(x)^2/120=1

We move all terms to the left:

36(x)^2/120-(1)=0

We multiply all the terms by the denominator


36x^2-1*120=0

We add all the numbers together, and all the variables

36x^2-120=0

a = 36; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·36·(-120)
Δ = 17280
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:

$\sqrt{\Delta}=\sqrt{17280}=\sqrt{576*30}=\sqrt{576}*\sqrt{30}=24\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{30}}{2*36}=\frac{0-24\sqrt{30}}{72}
=-\frac{24\sqrt{30}}{72}
=-\frac{\sqrt{30}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{30}}{2*36}=\frac{0+24\sqrt{30}}{72}
=\frac{24\sqrt{30}}{72}
=\frac{\sqrt{30}}{3}
$