32x-1/27x=243

Solution for 32x-1/27x=243 equation:

32x-1/27x=243

We move all terms to the left:

32x-1/27x-(243)=0


Domain of the equation: 27x!=0

x!=0/27

x!=0

x∈R


We multiply all the terms by the denominator


32x*27x-243*27x-1=0

Wy multiply elements

864x^2-6561x-1=0

a = 864; b = -6561; c = -1;
Δ = b2-4ac
Δ = -65612-4·864·(-1)
Δ = 43050177
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:

$\sqrt{\Delta}=\sqrt{43050177}=\sqrt{9*4783353}=\sqrt{9}*\sqrt{4783353}=3\sqrt{4783353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6561)-3\sqrt{4783353}}{2*864}=\frac{6561-3\sqrt{4783353}}{1728}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6561)+3\sqrt{4783353}}{2*864}=\frac{6561+3\sqrt{4783353}}{1728}
$