5-6n+4n=2-3n(2n-5)

Solution for 5-6n+4n=2-3n(2n-5) equation:

5-6n+4n=2-3n(2n-5)

We move all terms to the left:

5-6n+4n-(2-3n(2n-5))=0

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(2-3n(2n-5)), so:

2-3n(2n-5)

determiningTheFunctionDomain
-3n(2n-5)+2

We multiply parentheses

-6n^2+15n+2

Back to the equation:

-(-6n^2+15n+2)


We get rid of parentheses

6n^2-15n-2n-2+5=0

We add all the numbers together, and all the variables

6n^2-17n+3=0

a = 6; b = -17; c = +3;
Δ = b2-4ac
Δ = -172-4·6·3
Δ = 217
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{-(-17)-\sqrt{217}}{2*6}=\frac{17-\sqrt{217}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{217}}{2*6}=\frac{17+\sqrt{217}}{12}
$