20/3=6r2

Solution for 20/3=6r2 equation:

20/3=6r^2

We move all terms to the left:

20/3-(6r^2)=0

We multiply all the terms by the denominator


-6r^2*3+20=0

Wy multiply elements

-18r^2+20=0

a = -18; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-18)·20
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*-18}=\frac{0-12\sqrt{10}}{-36}
=-\frac{12\sqrt{10}}{-36}
=-\frac{\sqrt{10}}{-3}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*-18}=\frac{0+12\sqrt{10}}{-36}
=\frac{12\sqrt{10}}{-36}
=\frac{\sqrt{10}}{-3}
$