1/2(10+2n)=1/3(15n+15)

Solution for 1/2(10+2n)=1/3(15n+15) equation:

1/2(10+2n)=1/3(15n+15)

We move all terms to the left:

1/2(10+2n)-(1/3(15n+15))=0


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

n∈R



Domain of the equation: 3(15n+15))!=0

n∈R


We add all the numbers together, and all the variables

1/2(2n+10)-(1/3(15n+15))=0

We calculate fractions


(3n1/(2(2n+10)*3(15n+15)))+(-2n2/(2(2n+10)*3(15n+15)))=0


We calculate terms in parentheses: +(3n1/(2(2n+10)*3(15n+15))), so:

3n1/(2(2n+10)*3(15n+15))

We multiply all the terms by the denominator


3n1

We add all the numbers together, and all the variables

3n

Back to the equation:

+(3n)



We calculate terms in parentheses: +(-2n2/(2(2n+10)*3(15n+15))), so:

-2n2/(2(2n+10)*3(15n+15))

We multiply all the terms by the denominator


-2n2

We add all the numbers together, and all the variables

-2n^2

Back to the equation:

+(-2n^2)


We get rid of parentheses

-2n^2+3n=0

a = -2; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-2)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-2}=\frac{0}{-4}
=0
$