-(n+2)=15(n+7)n=

Solution for -(n+2)=15(n+7)n= equation:

-(n+2)=15(n+7)n=

We move all terms to the left:

-(n+2)-(15(n+7)n)=0

We get rid of parentheses

-n-(15(n+7)n)-2=0


We calculate terms in parentheses: -(15(n+7)n), so:

15(n+7)n

We multiply parentheses

15n^2+105n

Back to the equation:

-(15n^2+105n)


We add all the numbers together, and all the variables

-1n-(15n^2+105n)-2=0

We get rid of parentheses

-15n^2-1n-105n-2=0

We add all the numbers together, and all the variables

-15n^2-106n-2=0

a = -15; b = -106; c = -2;
Δ = b2-4ac
Δ = -1062-4·(-15)·(-2)
Δ = 11116
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:

$\sqrt{\Delta}=\sqrt{11116}=\sqrt{4*2779}=\sqrt{4}*\sqrt{2779}=2\sqrt{2779}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-2\sqrt{2779}}{2*-15}=\frac{106-2\sqrt{2779}}{-30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+2\sqrt{2779}}{2*-15}=\frac{106+2\sqrt{2779}}{-30}
$