1444+x^2=324x

Solution for 1444+x^2=324x equation:

1444+x^2=324x

We move all terms to the left:

1444+x^2-(324x)=0

a = 1; b = -324; c = +1444;
Δ = b2-4ac
Δ = -3242-4·1·1444
Δ = 99200
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:

$\sqrt{\Delta}=\sqrt{99200}=\sqrt{1600*62}=\sqrt{1600}*\sqrt{62}=40\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-40\sqrt{62}}{2*1}=\frac{324-40\sqrt{62}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+40\sqrt{62}}{2*1}=\frac{324+40\sqrt{62}}{2}
$