3r2=64-4r

Solution for 3r2=64-4r equation:

3r^2=64-4r

We move all terms to the left:

3r^2-(64-4r)=0

We add all the numbers together, and all the variables

3r^2-(-4r+64)=0

We get rid of parentheses

3r^2+4r-64=0

a = 3; b = 4; c = -64;
Δ = b2-4ac
Δ = 42-4·3·(-64)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-28}{2*3}=\frac{-32}{6}
=-5+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+28}{2*3}=\frac{24}{6}
=4
$