(3x-1)(1-7x)=0

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

(3x-1)(1-7x)=0

We add all the numbers together, and all the variables

(3x-1)(-7x+1)=0

We multiply parentheses ..

(-21x^2+3x+7x-1)=0

We get rid of parentheses

-21x^2+3x+7x-1=0

We add all the numbers together, and all the variables

-21x^2+10x-1=0

a = -21; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-21)·(-1)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*-21}=\frac{-14}{-42}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*-21}=\frac{-6}{-42}
=1/7
$