x^2-18x=54

Solution for x^2-18x=54 equation:

x^2-18x=54

We move all terms to the left:

x^2-18x-(54)=0

a = 1; b = -18; c = -54;
Δ = b2-4ac
Δ = -182-4·1·(-54)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{15}}{2*1}=\frac{18-6\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{15}}{2*1}=\frac{18+6\sqrt{15}}{2}
$