x^2=193

Solution for x^2=193 equation:

x^2=193

We move all terms to the left:

x^2-(193)=0

a = 1; b = 0; c = -193;
Δ = b2-4ac
Δ = 02-4·1·(-193)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{193}}{2*1}=\frac{0-2\sqrt{193}}{2}
=-\frac{2\sqrt{193}}{2}
=-\sqrt{193}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{193}}{2*1}=\frac{0+2\sqrt{193}}{2}
=\frac{2\sqrt{193}}{2}
=\sqrt{193}
$