19x2-20+5=0

Solution for 19x2-20+5=0 equation:

19x^2-20+5=0

We add all the numbers together, and all the variables

19x^2-15=0

a = 19; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·19·(-15)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{285}}{2*19}=\frac{0-2\sqrt{285}}{38}
=-\frac{2\sqrt{285}}{38}
=-\frac{\sqrt{285}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{285}}{2*19}=\frac{0+2\sqrt{285}}{38}
=\frac{2\sqrt{285}}{38}
=\frac{\sqrt{285}}{19}
$