23x^2=19

Solution for 23x^2=19 equation:

23x^2=19

We move all terms to the left:

23x^2-(19)=0

a = 23; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·23·(-19)
Δ = 1748
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:

$\sqrt{\Delta}=\sqrt{1748}=\sqrt{4*437}=\sqrt{4}*\sqrt{437}=2\sqrt{437}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{437}}{2*23}=\frac{0-2\sqrt{437}}{46}
=-\frac{2\sqrt{437}}{46}
=-\frac{\sqrt{437}}{23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{437}}{2*23}=\frac{0+2\sqrt{437}}{46}
=\frac{2\sqrt{437}}{46}
=\frac{\sqrt{437}}{23}
$