32(x^2+82x-522607)=0

Solution for 32(x^2+82x-522607)=0 equation:

32(x^2+82x-522607)=0

We multiply parentheses

32x^2+2624x-16723424=0

a = 32; b = 2624; c = -16723424;
Δ = b2-4ac
Δ = 26242-4·32·(-16723424)
Δ = 2147483648
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:

$\sqrt{\Delta}=\sqrt{2147483648}=\sqrt{1073741824*2}=\sqrt{1073741824}*\sqrt{2}=32768\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2624)-32768\sqrt{2}}{2*32}=\frac{-2624-32768\sqrt{2}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2624)+32768\sqrt{2}}{2*32}=\frac{-2624+32768\sqrt{2}}{64}
$