x^2=343.75

Solution for x^2=343.75 equation:

x^2=343.75

We move all terms to the left:

x^2-(343.75)=0

We add all the numbers together, and all the variables

x^2-343.75=0

a = 1; b = 0; c = -343.75;
Δ = b2-4ac
Δ = 02-4·1·(-343.75)
Δ = 1375
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:

$\sqrt{\Delta}=\sqrt{1375}=\sqrt{25*55}=\sqrt{25}*\sqrt{55}=5\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{55}}{2*1}=\frac{0-5\sqrt{55}}{2}
=-\frac{5\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{55}}{2*1}=\frac{0+5\sqrt{55}}{2}
=\frac{5\sqrt{55}}{2}
$