x^2-24x=128

Solution for x^2-24x=128 equation:

x^2-24x=128

We move all terms to the left:

x^2-24x-(128)=0

a = 1; b = -24; c = -128;
Δ = b2-4ac
Δ = -242-4·1·(-128)
Δ = 1088
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:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{17}}{2*1}=\frac{24-8\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{17}}{2*1}=\frac{24+8\sqrt{17}}{2}
$