(x-0.4)(3x-0.5)=0

Solution for (x-0.4)(3x-0.5)=0 equation:

(x-0.4)(3x-0.5)=0

We multiply parentheses ..

(+3x^2-0.5x-1.2x+0.2)=0

We get rid of parentheses

3x^2-0.5x-1.2x+0.2=0

We add all the numbers together, and all the variables

3x^2-1.7x+0.2=0

a = 3; b = -1.7; c = +0.2;
Δ = b2-4ac
Δ = -1.72-4·3·0.2
Δ = 0.49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.7)-\sqrt{0.49}}{2*3}=\frac{1.7-\sqrt{0.49}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.7)+\sqrt{0.49}}{2*3}=\frac{1.7+\sqrt{0.49}}{6}
$