(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^2-1r-7=0

a = 6; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·6·(-7)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*6}=\frac{-12}{12}
=-1
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*6}=\frac{14}{12}
=1+1/6
$