x^2-12x-44=9

Solution for x^2-12x-44=9 equation:

x^2-12x-44=9

We move all terms to the left:

x^2-12x-44-(9)=0

We add all the numbers together, and all the variables

x^2-12x-53=0

a = 1; b = -12; c = -53;
Δ = b2-4ac
Δ = -122-4·1·(-53)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{89}}{2*1}=\frac{12-2\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{89}}{2*1}=\frac{12+2\sqrt{89}}{2}
$