X^2+3x-81=243

Solution for X^2+3x-81=243 equation:

X^2+3X-81=243

We move all terms to the left:

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

We add all the numbers together, and all the variables

X^2+3X-324=0

a = 1; b = 3; c = -324;
Δ = b2-4ac
Δ = 32-4·1·(-324)
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{145}}{2*1}=\frac{-3-3\sqrt{145}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{145}}{2*1}=\frac{-3+3\sqrt{145}}{2}
$