a2+3a+1=0

Solution for a2+3a+1=0 equation:

a2+3a+1=0

We add all the numbers together, and all the variables

a^2+3a+1=0

a = 1; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·1·1
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{5}}{2*1}=\frac{-3-\sqrt{5}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{5}}{2*1}=\frac{-3+\sqrt{5}}{2}
$