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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2-22x+3=0

a = 7; b = -22; c = +3;
Δ = b2-4ac
Δ = -222-4·7·3
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-20}{2*7}=\frac{2}{14}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+20}{2*7}=\frac{42}{14}
=3
$