X2-2x-(45)2=128

Solution for X2-2x-(45)2=128 equation:

X2-2X-(45)2=128

We move all terms to the left:

X2-2X-(45)2-(128)=0

We add all the numbers together, and all the variables

X^2-2X-580=0

a = 1; b = -2; c = -580;
Δ = b2-4ac
Δ = -22-4·1·(-580)
Δ = 2324
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:

$\sqrt{\Delta}=\sqrt{2324}=\sqrt{4*581}=\sqrt{4}*\sqrt{581}=2\sqrt{581}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{581}}{2*1}=\frac{2-2\sqrt{581}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{581}}{2*1}=\frac{2+2\sqrt{581}}{2}
$