X^2+54x=729

Solution for X^2+54x=729 equation:

X^2+54X=729

We move all terms to the left:

X^2+54X-(729)=0

a = 1; b = 54; c = -729;
Δ = b2-4ac
Δ = 542-4·1·(-729)
Δ = 5832
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:

$\sqrt{\Delta}=\sqrt{5832}=\sqrt{2916*2}=\sqrt{2916}*\sqrt{2}=54\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54\sqrt{2}}{2*1}=\frac{-54-54\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54\sqrt{2}}{2*1}=\frac{-54+54\sqrt{2}}{2}
$