21r^2=16-16r

Solution for 21r^2=16-16r equation:

21r^2=16-16r

We move all terms to the left:

21r^2-(16-16r)=0

We add all the numbers together, and all the variables

21r^2-(-16r+16)=0

We get rid of parentheses

21r^2+16r-16=0

a = 21; b = 16; c = -16;
Δ = b2-4ac
Δ = 162-4·21·(-16)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-40}{2*21}=\frac{-56}{42}
=-1+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+40}{2*21}=\frac{24}{42}
=4/7
$