5n+19-2n=-4(n-10)5n+19-2n=-4(n-10)

Solution for 5n+19-2n=-4(n-10)5n+19-2n=-4(n-10) equation:

5n+19-2n=-4(n-10)5n+19-2n=-4(n-10)

We move all terms to the left:

5n+19-2n-(-4(n-10)5n+19-2n)=0

We add all the numbers together, and all the variables

3n-(-4(n-10)5n+19-2n)+19=0


We calculate terms in parentheses: -(-4(n-10)5n+19-2n), so:

-4(n-10)5n+19-2n

determiningTheFunctionDomain
-4(n-10)5n-2n+19

We add all the numbers together, and all the variables

-2n-4(n-10)5n+19

We multiply parentheses

-20n^2-2n+200n+19

We add all the numbers together, and all the variables

-20n^2+198n+19

Back to the equation:

-(-20n^2+198n+19)


We get rid of parentheses

20n^2-198n+3n-19+19=0

We add all the numbers together, and all the variables

20n^2-195n=0

a = 20; b = -195; c = 0;
Δ = b2-4ac
Δ = -1952-4·20·0
Δ = 38025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38025}=195$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-195)-195}{2*20}=\frac{0}{40}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-195)+195}{2*20}=\frac{390}{40}
=9+3/4
$