x^2=5^9

Solution for x^2=5^9 equation:

x^2=5^9

We move all terms to the left:

x^2-(5^9)=0

We add all the numbers together, and all the variables

x^2-1953125=0

a = 1; b = 0; c = -1953125;
Δ = b2-4ac
Δ = 02-4·1·(-1953125)
Δ = 7812500
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:

$\sqrt{\Delta}=\sqrt{7812500}=\sqrt{1562500*5}=\sqrt{1562500}*\sqrt{5}=1250\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1250\sqrt{5}}{2*1}=\frac{0-1250\sqrt{5}}{2}
=-\frac{1250\sqrt{5}}{2}
=-625\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1250\sqrt{5}}{2*1}=\frac{0+1250\sqrt{5}}{2}
=\frac{1250\sqrt{5}}{2}
=625\sqrt{5}
$