44800=1432x+x^2

Solution for 44800=1432x+x^2 equation:

44800=1432x+x^2

We move all terms to the left:

44800-(1432x+x^2)=0

We get rid of parentheses

-x^2-1432x+44800=0

We add all the numbers together, and all the variables

-1x^2-1432x+44800=0

a = -1; b = -1432; c = +44800;
Δ = b2-4ac
Δ = -14322-4·(-1)·44800
Δ = 2229824
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:

$\sqrt{\Delta}=\sqrt{2229824}=\sqrt{64*34841}=\sqrt{64}*\sqrt{34841}=8\sqrt{34841}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1432)-8\sqrt{34841}}{2*-1}=\frac{1432-8\sqrt{34841}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1432)+8\sqrt{34841}}{2*-1}=\frac{1432+8\sqrt{34841}}{-2}
$