5(n+2)=(3/5)*(5+10n)

Solution for 5(n+2)=(3/5)*(5+10n) equation:

5(n+2)=(3/5)(5+10n)

We move all terms to the left:

5(n+2)-((3/5)(5+10n))=0


Domain of the equation: 5)(5+10n))!=0

n∈R


We add all the numbers together, and all the variables

5(n+2)-((+3/5)(10n+5))=0

We multiply parentheses

5n-((+3/5)(10n+5))+10=0

We multiply parentheses ..

-((+30n^2+3/5*5))+5n+10=0

We multiply all the terms by the denominator


-((+30n^2+3+5n*5*5))+10*5*5))=0


We calculate terms in parentheses: -((+30n^2+3+5n*5*5)), so:

(+30n^2+3+5n*5*5)

We get rid of parentheses

30n^2+5n*5*5+3

Wy multiply elements

30n^2+125n*5+3

Wy multiply elements

30n^2+625n+3

Back to the equation:

-(30n^2+625n+3)


We add all the numbers together, and all the variables

-(30n^2+625n+3)=0

We get rid of parentheses

-30n^2-625n-3=0

a = -30; b = -625; c = -3;
Δ = b2-4ac
Δ = -6252-4·(-30)·(-3)
Δ = 390265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-625)-\sqrt{390265}}{2*-30}=\frac{625-\sqrt{390265}}{-60}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-625)+\sqrt{390265}}{2*-30}=\frac{625+\sqrt{390265}}{-60}
$