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

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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 $

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