8/9*n=4

Solution for 8/9*n=4 equation:

8/9*n=4

We move all terms to the left:

8/9*n-(4)=0


Domain of the equation: 9*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-4*9*n+8=0

Wy multiply elements

-36n*n+8=0

Wy multiply elements

-36n^2+8=0

a = -36; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-36)·8
Δ = 1152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-36}=\frac{0-24\sqrt{2}}{-72}
=-\frac{24\sqrt{2}}{-72}
=-\frac{\sqrt{2}}{-3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-36}=\frac{0+24\sqrt{2}}{-72}
=\frac{24\sqrt{2}}{-72}
=\frac{\sqrt{2}}{-3}
$