2a(5a+1)=0

Solution for 2a(5a+1)=0 equation:

2a(5a+1)=0

We multiply parentheses

10a^2+2a=0

a = 10; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·10·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*10}=\frac{-4}{20}
=-1/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*10}=\frac{0}{20}
=0
$