5a2-19=0

Solution for 5a2-19=0 equation:

5a^2-19=0

a = 5; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·5·(-19)
Δ = 380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{95}}{2*5}=\frac{0-2\sqrt{95}}{10}
=-\frac{2\sqrt{95}}{10}
=-\frac{\sqrt{95}}{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{95}}{2*5}=\frac{0+2\sqrt{95}}{10}
=\frac{2\sqrt{95}}{10}
=\frac{\sqrt{95}}{5}
$