x^2+4x+32=800

Solution for x^2+4x+32=800 equation:

x^2+4x+32=800

We move all terms to the left:

x^2+4x+32-(800)=0

We add all the numbers together, and all the variables

x^2+4x-768=0

a = 1; b = 4; c = -768;
Δ = b2-4ac
Δ = 42-4·1·(-768)
Δ = 3088
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:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{193}}{2*1}=\frac{-4-4\sqrt{193}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{193}}{2*1}=\frac{-4+4\sqrt{193}}{2}
$