21r(63r+3)=216

Solution for 21r(63r+3)=216 equation:

21r(63r+3)=216

We move all terms to the left:

21r(63r+3)-(216)=0

We multiply parentheses

1323r^2+63r-216=0

a = 1323; b = 63; c = -216;
Δ = b2-4ac
Δ = 632-4·1323·(-216)
Δ = 1147041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1147041}=1071$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-1071}{2*1323}=\frac{-1134}{2646}
=-3/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+1071}{2*1323}=\frac{1008}{2646}
=8/21
$