18-6n=-4n(-3n+2)-5n

Solution for 18-6n=-4n(-3n+2)-5n equation:

18-6n=-4n(-3n+2)-5n

We move all terms to the left:

18-6n-(-4n(-3n+2)-5n)=0


We calculate terms in parentheses: -(-4n(-3n+2)-5n), so:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

12n^2-5n-8n

We add all the numbers together, and all the variables

12n^2-13n

Back to the equation:

-(12n^2-13n)


We get rid of parentheses

-12n^2-6n+13n+18=0

We add all the numbers together, and all the variables

-12n^2+7n+18=0

a = -12; b = 7; c = +18;
Δ = b2-4ac
Δ = 72-4·(-12)·18
Δ = 913
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{-(7)-\sqrt{913}}{2*-12}=\frac{-7-\sqrt{913}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{913}}{2*-12}=\frac{-7+\sqrt{913}}{-24}
$