x.27(x-108)=54

Solution for x.27(x-108)=54 equation:

x.27(x-108)=54

We move all terms to the left:

x.27(x-108)-(54)=0

We multiply parentheses

x^2-108x-54=0

a = 1; b = -108; c = -54;
Δ = b2-4ac
Δ = -1082-4·1·(-54)
Δ = 11880
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:

$\sqrt{\Delta}=\sqrt{11880}=\sqrt{36*330}=\sqrt{36}*\sqrt{330}=6\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-6\sqrt{330}}{2*1}=\frac{108-6\sqrt{330}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+6\sqrt{330}}{2*1}=\frac{108+6\sqrt{330}}{2}
$