x2=343

Solution for x2=343 equation:

x2=343

We move all terms to the left:

x2-(343)=0

We add all the numbers together, and all the variables

x^2-343=0

a = 1; b = 0; c = -343;
Δ = b2-4ac
Δ = 02-4·1·(-343)
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{7}}{2*1}=\frac{0-14\sqrt{7}}{2}
=-\frac{14\sqrt{7}}{2}
=-7\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{7}}{2*1}=\frac{0+14\sqrt{7}}{2}
=\frac{14\sqrt{7}}{2}
=7\sqrt{7}
$