(X^2)+12x-81=3

Solution for (X^2)+12x-81=3 equation:

(X^2)+12X-81=3

We move all terms to the left:

(X^2)+12X-81-(3)=0

We add all the numbers together, and all the variables

X^2+12X-84=0

a = 1; b = 12; c = -84;
Δ = b2-4ac
Δ = 122-4·1·(-84)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{30}}{2*1}=\frac{-12-4\sqrt{30}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{30}}{2*1}=\frac{-12+4\sqrt{30}}{2}
$