x^2-12x=128

Solution for x^2-12x=128 equation:

x^2-12x=128

We move all terms to the left:

x^2-12x-(128)=0

a = 1; b = -12; c = -128;
Δ = b2-4ac
Δ = -122-4·1·(-128)
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{41}}{2*1}=\frac{12-4\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{41}}{2*1}=\frac{12+4\sqrt{41}}{2}
$