n-10=3(1/2n-10)

Solution for n-10=3(1/2n-10) equation:

n-10=3(1/2n-10)

We move all terms to the left:

n-10-(3(1/2n-10))=0


Domain of the equation: 2n-10))!=0

n∈R


We multiply all the terms by the denominator


n*2n-10*2n-10))-(3(1-10))=0

We add all the numbers together, and all the variables

n*2n-10*2n-10))-(3(-9))=0

We add all the numbers together, and all the variables

n*2n-10*2n=0

Wy multiply elements

2n^2-20n=0

a = 2; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·2·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*2}=\frac{0}{4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*2}=\frac{40}{4}
=10
$