(3a+1)(a-3)=0

Solution for (3a+1)(a-3)=0 equation:

(3a+1)(a-3)=0

We multiply parentheses ..

(+3a^2-9a+a-3)=0

We get rid of parentheses

3a^2-9a+a-3=0

We add all the numbers together, and all the variables

3a^2-8a-3=0

a = 3; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·3·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10}{2*3}=\frac{-2}{6}
=-1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*3}=\frac{18}{6}
=3
$