x2=49324

Solution for x2=49324 equation:

x2=49324

We move all terms to the left:

x2-(49324)=0

We add all the numbers together, and all the variables

x^2-49324=0

a = 1; b = 0; c = -49324;
Δ = b2-4ac
Δ = 02-4·1·(-49324)
Δ = 197296
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:

$\sqrt{\Delta}=\sqrt{197296}=\sqrt{16*12331}=\sqrt{16}*\sqrt{12331}=4\sqrt{12331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{12331}}{2*1}=\frac{0-4\sqrt{12331}}{2}
=-\frac{4\sqrt{12331}}{2}
=-2\sqrt{12331}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{12331}}{2*1}=\frac{0+4\sqrt{12331}}{2}
=\frac{4\sqrt{12331}}{2}
=2\sqrt{12331}
$