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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(-8(5n+6)3n-5), so:

-8(5n+6)3n-5

We multiply parentheses

-120n^2-144n-5

Back to the equation:

-(-120n^2-144n-5)


We get rid of parentheses

120n^2+144n+3n+5-5=0

We add all the numbers together, and all the variables

120n^2+147n=0

a = 120; b = 147; c = 0;
Δ = b2-4ac
Δ = 1472-4·120·0
Δ = 21609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21609}=147$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(147)-147}{2*120}=\frac{-294}{240}
=-1+9/40
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(147)+147}{2*120}=\frac{0}{240}
=0
$