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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6r^2-13r+7=0

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

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