(1/3)x=27x-4

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

(1/3)x=27x-4

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

x^2-(27x-4)=0

We get rid of parentheses

x^2-27x+4=0

a = 1; b = -27; c = +4;
Δ = b2-4ac
Δ = -272-4·1·4
Δ = 713
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{713}}{2*1}=\frac{27-\sqrt{713}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{713}}{2*1}=\frac{27+\sqrt{713}}{2}
$