243(x+3)=81(x2)

Solution for 243(x+3)=81(x2) equation:

243(x+3)=81(x2)

We move all terms to the left:

243(x+3)-(81(x2))=0

determiningTheFunctionDomain
243(x+3)-81x2=0

We add all the numbers together, and all the variables

-81x^2+243(x+3)=0

We multiply parentheses

-81x^2+243x+729=0

a = -81; b = 243; c = +729;
Δ = b2-4ac
Δ = 2432-4·(-81)·729
Δ = 295245
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:

$\sqrt{\Delta}=\sqrt{295245}=\sqrt{59049*5}=\sqrt{59049}*\sqrt{5}=243\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(243)-243\sqrt{5}}{2*-81}=\frac{-243-243\sqrt{5}}{-162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(243)+243\sqrt{5}}{2*-81}=\frac{-243+243\sqrt{5}}{-162}
$