X^2-6=108x

Solution for X^2-6=108x equation:

X^2-6=108X

We move all terms to the left:

X^2-6-(108X)=0

a = 1; b = -108; c = -6;
Δ = b2-4ac
Δ = -1082-4·1·(-6)
Δ = 11688
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:

$\sqrt{\Delta}=\sqrt{11688}=\sqrt{4*2922}=\sqrt{4}*\sqrt{2922}=2\sqrt{2922}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{2922}}{2*1}=\frac{108-2\sqrt{2922}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{2922}}{2*1}=\frac{108+2\sqrt{2922}}{2}
$