0=5a^2+7a+1

Solution for 0=5a^2+7a+1 equation:

0=5a^2+7a+1

We move all terms to the left:

0-(5a^2+7a+1)=0

We add all the numbers together, and all the variables

-(5a^2+7a+1)=0

We get rid of parentheses

-5a^2-7a-1=0

a = -5; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·(-5)·(-1)
Δ = 29
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{-(-7)-\sqrt{29}}{2*-5}=\frac{7-\sqrt{29}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{29}}{2*-5}=\frac{7+\sqrt{29}}{-10}
$