2(x^2-5500x-360000)=0

Solution for 2(x^2-5500x-360000)=0 equation:

2(x^2-5500x-360000)=0

We multiply parentheses

2x^2-11000x-720000=0

a = 2; b = -11000; c = -720000;
Δ = b2-4ac
Δ = -110002-4·2·(-720000)
Δ = 126760000
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:

$\sqrt{\Delta}=\sqrt{126760000}=\sqrt{40000*3169}=\sqrt{40000}*\sqrt{3169}=200\sqrt{3169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11000)-200\sqrt{3169}}{2*2}=\frac{11000-200\sqrt{3169}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11000)+200\sqrt{3169}}{2*2}=\frac{11000+200\sqrt{3169}}{4}
$