5x^2+1=381

Solution for 5x^2+1=381 equation:

5x^2+1=381

We move all terms to the left:

5x^2+1-(381)=0

We add all the numbers together, and all the variables

5x^2-380=0

a = 5; b = 0; c = -380;
Δ = b2-4ac
Δ = 02-4·5·(-380)
Δ = 7600
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:

$\sqrt{\Delta}=\sqrt{7600}=\sqrt{400*19}=\sqrt{400}*\sqrt{19}=20\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{19}}{2*5}=\frac{0-20\sqrt{19}}{10}
=-\frac{20\sqrt{19}}{10}
=-2\sqrt{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{19}}{2*5}=\frac{0+20\sqrt{19}}{10}
=\frac{20\sqrt{19}}{10}
=2\sqrt{19}
$