(7r+1)(r-12)=0

Solution for (7r+1)(r-12)=0 equation:

(7r+1)(r-12)=0

We multiply parentheses ..

(+7r^2-84r+r-12)=0

We get rid of parentheses

7r^2-84r+r-12=0

We add all the numbers together, and all the variables

7r^2-83r-12=0

a = 7; b = -83; c = -12;
Δ = b2-4ac
Δ = -832-4·7·(-12)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-85}{2*7}=\frac{-2}{14}
=-1/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+85}{2*7}=\frac{168}{14}
=12
$