0=9a^2+46a+5

Solution for 0=9a^2+46a+5 equation:

0=9a^2+46a+5

We move all terms to the left:

0-(9a^2+46a+5)=0

We add all the numbers together, and all the variables

-(9a^2+46a+5)=0

We get rid of parentheses

-9a^2-46a-5=0

a = -9; b = -46; c = -5;
Δ = b2-4ac
Δ = -462-4·(-9)·(-5)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-44}{2*-9}=\frac{2}{-18}
=-1/9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+44}{2*-9}=\frac{90}{-18}
=-5
$