2a(7a-1)=0

Solution for 2a(7a-1)=0 equation:

2a(7a-1)=0

We multiply parentheses

14a^2-2a=0

a = 14; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·14·0
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*14}=\frac{0}{28}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*14}=\frac{4}{28}
=1/7
$