32/6=5r2

Solution for 32/6=5r2 equation:

32/6=5r^2

We move all terms to the left:

32/6-(5r^2)=0

We multiply all the terms by the denominator


-5r^2*6+32=0

Wy multiply elements

-30r^2+32=0

a = -30; b = 0; c = +32;
Δ = b2-4ac
Δ = 02-4·(-30)·32
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*-30}=\frac{0-16\sqrt{15}}{-60}
=-\frac{16\sqrt{15}}{-60}
=-\frac{4\sqrt{15}}{-15}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*-30}=\frac{0+16\sqrt{15}}{-60}
=\frac{16\sqrt{15}}{-60}
=\frac{4\sqrt{15}}{-15}
$