(3r-21)(21r-3)=0

Solution for (3r-21)(21r-3)=0 equation:

(3r-21)(21r-3)=0

We multiply parentheses ..

(+63r^2-9r-441r+63)=0

We get rid of parentheses

63r^2-9r-441r+63=0

We add all the numbers together, and all the variables

63r^2-450r+63=0

a = 63; b = -450; c = +63;
Δ = b2-4ac
Δ = -4502-4·63·63
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-432}{2*63}=\frac{18}{126}
=1/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+432}{2*63}=\frac{882}{126}
=7
$