16n/8n+10-2n*3-8=22

Solution for 16n/8n+10-2n*3-8=22 equation:

16n/8n+10-2n*3-8=22

We move all terms to the left:

16n/8n+10-2n*3-8-(22)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R


We add all the numbers together, and all the variables

16n/8n-2n*3-20=0

Wy multiply elements

16n/8n-6n-20=0

We multiply all the terms by the denominator


16n-6n*8n-20*8n=0

Wy multiply elements

-48n^2+16n-160n=0

We add all the numbers together, and all the variables

-48n^2-144n=0

a = -48; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·(-48)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*-48}=\frac{0}{-96}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*-48}=\frac{288}{-96}
=-3
$