-4320+x^2/4-6x/4=0

Solution for -4320+x^2/4-6x/4=0 equation:

-4320+x^2/4-6x/4=0

We multiply all the terms by the denominator


x^2-6x-4320*4=0

We add all the numbers together, and all the variables

x^2-6x-17280=0

a = 1; b = -6; c = -17280;
Δ = b2-4ac
Δ = -62-4·1·(-17280)
Δ = 69156
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:

$\sqrt{\Delta}=\sqrt{69156}=\sqrt{36*1921}=\sqrt{36}*\sqrt{1921}=6\sqrt{1921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{1921}}{2*1}=\frac{6-6\sqrt{1921}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{1921}}{2*1}=\frac{6+6\sqrt{1921}}{2}
$