-10+5n=6(2n+9)n

Solution for -10+5n=6(2n+9)n equation:

-10+5n=6(2n+9)n

We move all terms to the left:

-10+5n-(6(2n+9)n)=0


We calculate terms in parentheses: -(6(2n+9)n), so:

6(2n+9)n

We multiply parentheses

12n^2+54n

Back to the equation:

-(12n^2+54n)


We get rid of parentheses

-12n^2+5n-54n-10=0

We add all the numbers together, and all the variables

-12n^2-49n-10=0

a = -12; b = -49; c = -10;
Δ = b2-4ac
Δ = -492-4·(-12)·(-10)
Δ = 1921
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{-(-49)-\sqrt{1921}}{2*-12}=\frac{49-\sqrt{1921}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{1921}}{2*-12}=\frac{49+\sqrt{1921}}{-24}
$