-10=2n+14/3n

Solution for -10=2n+14/3n equation:

-10=2n+14/3n

We move all terms to the left:

-10-(2n+14/3n)=0


Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-(+2n+14/3n)-10=0

We get rid of parentheses

-2n-14/3n-10=0

We multiply all the terms by the denominator


-2n*3n-10*3n-14=0

Wy multiply elements

-6n^2-30n-14=0

a = -6; b = -30; c = -14;
Δ = b2-4ac
Δ = -302-4·(-6)·(-14)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{141}}{2*-6}=\frac{30-2\sqrt{141}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{141}}{2*-6}=\frac{30+2\sqrt{141}}{-12}
$