(x-7)(6x-1)=0

Solution for (x-7)(6x-1)=0 equation:

(x-7)(6x-1)=0

We multiply parentheses ..

(+6x^2-1x-42x+7)=0

We get rid of parentheses

6x^2-1x-42x+7=0

We add all the numbers together, and all the variables

6x^2-43x+7=0

a = 6; b = -43; c = +7;
Δ = b2-4ac
Δ = -432-4·6·7
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-41}{2*6}=\frac{2}{12}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+41}{2*6}=\frac{84}{12}
=7
$