5a^2+3a+1=3a^2

Solution for 5a^2+3a+1=3a^2 equation:

5a^2+3a+1=3a^2

We move all terms to the left:

5a^2+3a+1-(3a^2)=0

determiningTheFunctionDomain
5a^2-3a^2+3a+1=0

We add all the numbers together, and all the variables

2a^2+3a+1=0

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

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-1}{2*2}=\frac{-4}{4}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+1}{2*2}=\frac{-2}{4}
=-1/2
$