14/3=r2

Solution for 14/3=r2 equation:

14/3=r2

We move all terms to the left:

14/3-(r2)=0

We add all the numbers together, and all the variables

-1r^2+14/3=0

We multiply all the terms by the denominator


-1r^2*3+14=0

Wy multiply elements

-3r^2+14=0

a = -3; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-3)·14
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*-3}=\frac{0-2\sqrt{42}}{-6}
=-\frac{2\sqrt{42}}{-6}
=-\frac{\sqrt{42}}{-3}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*-3}=\frac{0+2\sqrt{42}}{-6}
=\frac{2\sqrt{42}}{-6}
=\frac{\sqrt{42}}{-3}
$