1/9=27^2x-4

Solution for 1/9=27^2x-4 equation:

1/9=27^2x-4

We move all terms to the left:

1/9-(27^2x-4)=0

We get rid of parentheses

-27^2x+4+1/9=0

We multiply all the terms by the denominator


-27^2x*9+1+4*9=0

We add all the numbers together, and all the variables

-27^2x*9+37=0

Wy multiply elements

-243x^2+37=0

a = -243; b = 0; c = +37;
Δ = b2-4ac
Δ = 02-4·(-243)·37
Δ = 35964
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:

$\sqrt{\Delta}=\sqrt{35964}=\sqrt{324*111}=\sqrt{324}*\sqrt{111}=18\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{111}}{2*-243}=\frac{0-18\sqrt{111}}{-486}
=-\frac{18\sqrt{111}}{-486}
=-\frac{\sqrt{111}}{-27}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{111}}{2*-243}=\frac{0+18\sqrt{111}}{-486}
=\frac{18\sqrt{111}}{-486}
=\frac{\sqrt{111}}{-27}
$