19x^2=9

Solution for 19x^2=9 equation:

19x^2=9

We move all terms to the left:

19x^2-(9)=0

a = 19; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·19·(-9)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{19}}{2*19}=\frac{0-6\sqrt{19}}{38}
=-\frac{6\sqrt{19}}{38}
=-\frac{3\sqrt{19}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{19}}{2*19}=\frac{0+6\sqrt{19}}{38}
=\frac{6\sqrt{19}}{38}
=\frac{3\sqrt{19}}{19}
$