17*x^2=19

Solution for 17*x^2=19 equation:

17x^2=19

We move all terms to the left:

17x^2-(19)=0

a = 17; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·17·(-19)
Δ = 1292
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:

$\sqrt{\Delta}=\sqrt{1292}=\sqrt{4*323}=\sqrt{4}*\sqrt{323}=2\sqrt{323}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{323}}{2*17}=\frac{0-2\sqrt{323}}{34}
=-\frac{2\sqrt{323}}{34}
=-\frac{\sqrt{323}}{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{323}}{2*17}=\frac{0+2\sqrt{323}}{34}
=\frac{2\sqrt{323}}{34}
=\frac{\sqrt{323}}{17}
$