N/10n=5n+10

Solution for N/10n=5n+10 equation:

/10N=5N+10

We move all terms to the left:

/10N-(5N+10)=0


Domain of the equation: 10N!=0

N!=0/10

N!=0

N∈R


We get rid of parentheses

/10N-5N-10=0

We multiply all the terms by the denominator


-5N*10N-10*10N+=0

We add all the numbers together, and all the variables

-5N*10N-10*10N=0

Wy multiply elements

-50N^2-100N=0

a = -50; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·(-50)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*-50}=\frac{0}{-100}
=0
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*-50}=\frac{200}{-100}
=-2
$