-10-5n+2=2-21/2n

Solution for -10-5n+2=2-21/2n equation:

-10-5n+2=2-21/2n

We move all terms to the left:

-10-5n+2-(2-21/2n)=0


Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-5n-(-21/2n+2)-10+2=0

We add all the numbers together, and all the variables

-5n-(-21/2n+2)-8=0

We get rid of parentheses

-5n+21/2n-2-8=0

We multiply all the terms by the denominator


-5n*2n-2*2n-8*2n+21=0

Wy multiply elements

-10n^2-4n-16n+21=0

We add all the numbers together, and all the variables

-10n^2-20n+21=0

a = -10; b = -20; c = +21;
Δ = b2-4ac
Δ = -202-4·(-10)·21
Δ = 1240
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:

$\sqrt{\Delta}=\sqrt{1240}=\sqrt{4*310}=\sqrt{4}*\sqrt{310}=2\sqrt{310}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{310}}{2*-10}=\frac{20-2\sqrt{310}}{-20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{310}}{2*-10}=\frac{20+2\sqrt{310}}{-20}
$