X^2-18x=1440^2

Solution for X^2-18x=1440^2 equation:

X^2-18X=1440^2

We move all terms to the left:

X^2-18X-(1440^2)=0

We add all the numbers together, and all the variables

X^2-18X-2073600=0

a = 1; b = -18; c = -2073600;
Δ = b2-4ac
Δ = -182-4·1·(-2073600)
Δ = 8294724
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:

$\sqrt{\Delta}=\sqrt{8294724}=\sqrt{324*25601}=\sqrt{324}*\sqrt{25601}=18\sqrt{25601}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{25601}}{2*1}=\frac{18-18\sqrt{25601}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{25601}}{2*1}=\frac{18+18\sqrt{25601}}{2}
$