1/36=6^2x-4

Solution for 1/36=6^2x-4 equation:

1/36=6^2x-4

We move all terms to the left:

1/36-(6^2x-4)=0

We get rid of parentheses

-6^2x+4+1/36=0

We multiply all the terms by the denominator


-6^2x*36+1+4*36=0

We add all the numbers together, and all the variables

-6^2x*36+145=0

Wy multiply elements

-216x^2+145=0

a = -216; b = 0; c = +145;
Δ = b2-4ac
Δ = 02-4·(-216)·145
Δ = 125280
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:

$\sqrt{\Delta}=\sqrt{125280}=\sqrt{144*870}=\sqrt{144}*\sqrt{870}=12\sqrt{870}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{870}}{2*-216}=\frac{0-12\sqrt{870}}{-432}
=-\frac{12\sqrt{870}}{-432}
=-\frac{\sqrt{870}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{870}}{2*-216}=\frac{0+12\sqrt{870}}{-432}
=\frac{12\sqrt{870}}{-432}
=\frac{\sqrt{870}}{-36}
$