(1/3x)=27x-4

Solution for (1/3x)=27x-4 equation:

(1/3x)=27x-4

We move all terms to the left:

(1/3x)-(27x-4)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3x)-(27x-4)=0

We get rid of parentheses

1/3x-27x+4=0

We multiply all the terms by the denominator


-27x*3x+4*3x+1=0

Wy multiply elements

-81x^2+12x+1=0

a = -81; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-81)·1
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{13}}{2*-81}=\frac{-12-6\sqrt{13}}{-162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{13}}{2*-81}=\frac{-12+6\sqrt{13}}{-162}
$