(3x-1)(20x-50)=0

Solution for (3x-1)(20x-50)=0 equation:

(3x-1)(20x-50)=0

We multiply parentheses ..

(+60x^2-150x-20x+50)=0

We get rid of parentheses

60x^2-150x-20x+50=0

We add all the numbers together, and all the variables

60x^2-170x+50=0

a = 60; b = -170; c = +50;
Δ = b2-4ac
Δ = -1702-4·60·50
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-130}{2*60}=\frac{40}{120}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+130}{2*60}=\frac{300}{120}
=2+1/2
$