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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2-13x+6=0

a = 7; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·7·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-1}{2*7}=\frac{12}{14}
=6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*7}=\frac{14}{14}
=1
$