X(x-3)=54^2

Solution for X(x-3)=54^2 equation:

X(X-3)=54^2

We move all terms to the left:

X(X-3)-(54^2)=0

We add all the numbers together, and all the variables

X(X-3)-2916=0

We multiply parentheses

X^2-3X-2916=0

a = 1; b = -3; c = -2916;
Δ = b2-4ac
Δ = -32-4·1·(-2916)
Δ = 11673
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:

$\sqrt{\Delta}=\sqrt{11673}=\sqrt{9*1297}=\sqrt{9}*\sqrt{1297}=3\sqrt{1297}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{1297}}{2*1}=\frac{3-3\sqrt{1297}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{1297}}{2*1}=\frac{3+3\sqrt{1297}}{2}
$