x^2-444x=-6000

Solution for x^2-444x=-6000 equation:

x^2-444x=-6000

We move all terms to the left:

x^2-444x-(-6000)=0

We add all the numbers together, and all the variables

x^2-444x+6000=0

a = 1; b = -444; c = +6000;
Δ = b2-4ac
Δ = -4442-4·1·6000
Δ = 173136
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:

$\sqrt{\Delta}=\sqrt{173136}=\sqrt{16*10821}=\sqrt{16}*\sqrt{10821}=4\sqrt{10821}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-444)-4\sqrt{10821}}{2*1}=\frac{444-4\sqrt{10821}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-444)+4\sqrt{10821}}{2*1}=\frac{444+4\sqrt{10821}}{2}
$