X^2-96x+108=0

Solution for X^2-96x+108=0 equation:

X^2-96X+108=0

a = 1; b = -96; c = +108;
Δ = b2-4ac
Δ = -962-4·1·108
Δ = 8784
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:

$\sqrt{\Delta}=\sqrt{8784}=\sqrt{144*61}=\sqrt{144}*\sqrt{61}=12\sqrt{61}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-12\sqrt{61}}{2*1}=\frac{96-12\sqrt{61}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+12\sqrt{61}}{2*1}=\frac{96+12\sqrt{61}}{2}
$