4/5n+6=-n-52/2

Solution for 4/5n+6=-n-52/2 equation:

4/5n+6=-n-52/2

We move all terms to the left:

4/5n+6-(-n-52/2)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

4/5n-(-1n-26)+6=0

We get rid of parentheses

4/5n+1n+26+6=0

We multiply all the terms by the denominator


1n*5n+26*5n+6*5n+4=0

Wy multiply elements

5n^2+130n+30n+4=0

We add all the numbers together, and all the variables

5n^2+160n+4=0

a = 5; b = 160; c = +4;
Δ = b2-4ac
Δ = 1602-4·5·4
Δ = 25520
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:

$\sqrt{\Delta}=\sqrt{25520}=\sqrt{16*1595}=\sqrt{16}*\sqrt{1595}=4\sqrt{1595}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-4\sqrt{1595}}{2*5}=\frac{-160-4\sqrt{1595}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+4\sqrt{1595}}{2*5}=\frac{-160+4\sqrt{1595}}{10}
$