14x^2=19

Solution for 14x^2=19 equation:

14x^2=19

We move all terms to the left:

14x^2-(19)=0

a = 14; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·14·(-19)
Δ = 1064
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:

$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{266}}{2*14}=\frac{0-2\sqrt{266}}{28}
=-\frac{2\sqrt{266}}{28}
=-\frac{\sqrt{266}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{266}}{2*14}=\frac{0+2\sqrt{266}}{28}
=\frac{2\sqrt{266}}{28}
=\frac{\sqrt{266}}{14}
$