23x^2=31

Solution for 23x^2=31 equation:

23x^2=31

We move all terms to the left:

23x^2-(31)=0

a = 23; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·23·(-31)
Δ = 2852
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:

$\sqrt{\Delta}=\sqrt{2852}=\sqrt{4*713}=\sqrt{4}*\sqrt{713}=2\sqrt{713}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{713}}{2*23}=\frac{0-2\sqrt{713}}{46}
=-\frac{2\sqrt{713}}{46}
=-\frac{\sqrt{713}}{23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{713}}{2*23}=\frac{0+2\sqrt{713}}{46}
=\frac{2\sqrt{713}}{46}
=\frac{\sqrt{713}}{23}
$