6r(r-7)=0

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

6r(r-7)=0

We multiply parentheses

6r^2-42r=0

a = 6; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·6·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*6}=\frac{0}{12}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*6}=\frac{84}{12}
=7
$