3(7r-2)21r=6

Solution for 3(7r-2)21r=6 equation:

3(7r-2)21r=6

We move all terms to the left:

3(7r-2)21r-(6)=0

We multiply parentheses

441r^2-126r-6=0

a = 441; b = -126; c = -6;
Δ = b2-4ac
Δ = -1262-4·441·(-6)
Δ = 26460
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{26460}=\sqrt{1764*15}=\sqrt{1764}*\sqrt{15}=42\sqrt{15}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-42\sqrt{15}}{2*441}=\frac{126-42\sqrt{15}}{882}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+42\sqrt{15}}{2*441}=\frac{126+42\sqrt{15}}{882}
$