3x(10^x-1)=0

Solution for 3x(10^x-1)=0 equation:

3x(10^x-1)=0

We multiply parentheses

30x^2-3x=0

a = 30; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·30·0
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*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*30}=\frac{6}{60}
=1/10
$