8/3n^2=6

Solution for 8/3n^2=6 equation:

8/3n^2=6

We move all terms to the left:

8/3n^2-(6)=0


Domain of the equation: 3n^2!=0

n^2!=0/3

n^2!=√0

n!=0

n∈R


We multiply all the terms by the denominator


-6*3n^2+8=0

Wy multiply elements

-18n^2+8=0

a = -18; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-18)·8
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-18}=\frac{-24}{-36}
=2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-18}=\frac{24}{-36}
=-2/3
$