x^2-12x-44=100

Solution for x^2-12x-44=100 equation:

x^2-12x-44=100

We move all terms to the left:

x^2-12x-44-(100)=0

We add all the numbers together, and all the variables

x^2-12x-144=0

a = 1; b = -12; c = -144;
Δ = b2-4ac
Δ = -122-4·1·(-144)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{5}}{2*1}=\frac{12-12\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{5}}{2*1}=\frac{12+12\sqrt{5}}{2}
$