x2=431

Solution for x2=431 equation:

x2=431

We move all terms to the left:

x2-(431)=0

We add all the numbers together, and all the variables

x^2-431=0

a = 1; b = 0; c = -431;
Δ = b2-4ac
Δ = 02-4·1·(-431)
Δ = 1724
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:

$\sqrt{\Delta}=\sqrt{1724}=\sqrt{4*431}=\sqrt{4}*\sqrt{431}=2\sqrt{431}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{431}}{2*1}=\frac{0-2\sqrt{431}}{2}
=-\frac{2\sqrt{431}}{2}
=-\sqrt{431}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{431}}{2*1}=\frac{0+2\sqrt{431}}{2}
=\frac{2\sqrt{431}}{2}
=\sqrt{431}
$