5+19x2=48

Solution for 5+19x2=48 equation:

5+19x^2=48

We move all terms to the left:

5+19x^2-(48)=0

We add all the numbers together, and all the variables

19x^2-43=0

a = 19; b = 0; c = -43;
Δ = b2-4ac
Δ = 02-4·19·(-43)
Δ = 3268
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:

$\sqrt{\Delta}=\sqrt{3268}=\sqrt{4*817}=\sqrt{4}*\sqrt{817}=2\sqrt{817}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{817}}{2*19}=\frac{0-2\sqrt{817}}{38}
=-\frac{2\sqrt{817}}{38}
=-\frac{\sqrt{817}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{817}}{2*19}=\frac{0+2\sqrt{817}}{38}
=\frac{2\sqrt{817}}{38}
=\frac{\sqrt{817}}{19}
$