-16+5n=-7(-6+8n)3n

Solution for -16+5n=-7(-6+8n)3n equation:

-16+5n=-7(-6+8n)3n

We move all terms to the left:

-16+5n-(-7(-6+8n)3n)=0

We add all the numbers together, and all the variables

5n-(-7(8n-6)3n)-16=0


We calculate terms in parentheses: -(-7(8n-6)3n), so:

-7(8n-6)3n

We multiply parentheses

-168n^2+126n

Back to the equation:

-(-168n^2+126n)


We get rid of parentheses

168n^2-126n+5n-16=0

We add all the numbers together, and all the variables

168n^2-121n-16=0

a = 168; b = -121; c = -16;
Δ = b2-4ac
Δ = -1212-4·168·(-16)
Δ = 25393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-121)-\sqrt{25393}}{2*168}=\frac{121-\sqrt{25393}}{336}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-121)+\sqrt{25393}}{2*168}=\frac{121+\sqrt{25393}}{336}
$