5+19x2=43

Solution for 5+19x2=43 equation:

5+19x^2=43

We move all terms to the left:

5+19x^2-(43)=0

We add all the numbers together, and all the variables

19x^2-38=0

a = 19; b = 0; c = -38;
Δ = b2-4ac
Δ = 02-4·19·(-38)
Δ = 2888
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:

$\sqrt{\Delta}=\sqrt{2888}=\sqrt{1444*2}=\sqrt{1444}*\sqrt{2}=38\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-38\sqrt{2}}{2*19}=\frac{0-38\sqrt{2}}{38}
=-\frac{38\sqrt{2}}{38}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+38\sqrt{2}}{2*19}=\frac{0+38\sqrt{2}}{38}
=\frac{38\sqrt{2}}{38}
=\sqrt{2}
$