X(x-54)=180

Solution for X(x-54)=180 equation:

X(X-54)=180

We move all terms to the left:

X(X-54)-(180)=0

We multiply parentheses

X^2-54X-180=0

a = 1; b = -54; c = -180;
Δ = b2-4ac
Δ = -542-4·1·(-180)
Δ = 3636
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:

$\sqrt{\Delta}=\sqrt{3636}=\sqrt{36*101}=\sqrt{36}*\sqrt{101}=6\sqrt{101}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{101}}{2*1}=\frac{54-6\sqrt{101}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{101}}{2*1}=\frac{54+6\sqrt{101}}{2}
$