3x(7x+1)=0

Solution for 3x(7x+1)=0 equation:

3x(7x+1)=0

We multiply parentheses

21x^2+3x=0

a = 21; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·21·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*21}=\frac{-6}{42}
=-1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*21}=\frac{0}{42}
=0
$