x^2-444x=-12000

Solution for x^2-444x=-12000 equation:

x^2-444x=-12000

We move all terms to the left:

x^2-444x-(-12000)=0

We add all the numbers together, and all the variables

x^2-444x+12000=0

a = 1; b = -444; c = +12000;
Δ = b2-4ac
Δ = -4442-4·1·12000
Δ = 149136
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:

$\sqrt{\Delta}=\sqrt{149136}=\sqrt{16*9321}=\sqrt{16}*\sqrt{9321}=4\sqrt{9321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-444)-4\sqrt{9321}}{2*1}=\frac{444-4\sqrt{9321}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-444)+4\sqrt{9321}}{2*1}=\frac{444+4\sqrt{9321}}{2}
$