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

Solution for (6r+7)(r-2)=0 equation:

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

We multiply parentheses ..

(+6r^2-12r+7r-14)=0

We get rid of parentheses

6r^2-12r+7r-14=0

We add all the numbers together, and all the variables

6r^2-5r-14=0

a = 6; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·6·(-14)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*6}=\frac{-14}{12}
=-1+1/6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*6}=\frac{24}{12}
=2
$