x^2=49576

Solution for x^2=49576 equation:

x^2=49576

We move all terms to the left:

x^2-(49576)=0

a = 1; b = 0; c = -49576;
Δ = b2-4ac
Δ = 02-4·1·(-49576)
Δ = 198304
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:

$\sqrt{\Delta}=\sqrt{198304}=\sqrt{16*12394}=\sqrt{16}*\sqrt{12394}=4\sqrt{12394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{12394}}{2*1}=\frac{0-4\sqrt{12394}}{2}
=-\frac{4\sqrt{12394}}{2}
=-2\sqrt{12394}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{12394}}{2*1}=\frac{0+4\sqrt{12394}}{2}
=\frac{4\sqrt{12394}}{2}
=2\sqrt{12394}
$