0=3x^2+8x+1

Solution for 0=3x^2+8x+1 equation:

0=3x^2+8x+1

We move all terms to the left:

0-(3x^2+8x+1)=0

We add all the numbers together, and all the variables

-(3x^2+8x+1)=0

We get rid of parentheses

-3x^2-8x-1=0

a = -3; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·(-3)·(-1)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{13}}{2*-3}=\frac{8-2\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{13}}{2*-3}=\frac{8+2\sqrt{13}}{-6}
$