12^2x-4=1/144

Solution for 12^2x-4=1/144 equation:

12^2x-4=1/144

We move all terms to the left:

12^2x-4-(1/144)=0

We add all the numbers together, and all the variables

12^2x-4-(+1/144)=0

We get rid of parentheses

12^2x-4-1/144=0

We multiply all the terms by the denominator


12^2x*144-1-4*144=0

We add all the numbers together, and all the variables

12^2x*144-577=0

Wy multiply elements

1728x^2-577=0

a = 1728; b = 0; c = -577;
Δ = b2-4ac
Δ = 02-4·1728·(-577)
Δ = 3988224
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:

$\sqrt{\Delta}=\sqrt{3988224}=\sqrt{2304*1731}=\sqrt{2304}*\sqrt{1731}=48\sqrt{1731}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{1731}}{2*1728}=\frac{0-48\sqrt{1731}}{3456}
=-\frac{48\sqrt{1731}}{3456}
=-\frac{\sqrt{1731}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{1731}}{2*1728}=\frac{0+48\sqrt{1731}}{3456}
=\frac{48\sqrt{1731}}{3456}
=\frac{\sqrt{1731}}{72}
$