(123)10=(x)2

Solution for (123)10=(x)2 equation:

(123)10=(x)2

We move all terms to the left:

(123)10-((x)2)=0

determiningTheFunctionDomain
-x2+12310=0

We add all the numbers together, and all the variables

-1x^2+12310=0

a = -1; b = 0; c = +12310;
Δ = b2-4ac
Δ = 02-4·(-1)·12310
Δ = 49240
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:

$\sqrt{\Delta}=\sqrt{49240}=\sqrt{4*12310}=\sqrt{4}*\sqrt{12310}=2\sqrt{12310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{12310}}{2*-1}=\frac{0-2\sqrt{12310}}{-2}
=-\frac{2\sqrt{12310}}{-2}
=-\frac{\sqrt{12310}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{12310}}{2*-1}=\frac{0+2\sqrt{12310}}{-2}
=\frac{2\sqrt{12310}}{-2}
=\frac{\sqrt{12310}}{-1}
$