9+9(1-2n)=8n(3n+7)

Solution for 9+9(1-2n)=8n(3n+7) equation:

9+9(1-2n)=8n(3n+7)

We move all terms to the left:

9+9(1-2n)-(8n(3n+7))=0

We add all the numbers together, and all the variables

9(-2n+1)-(8n(3n+7))+9=0

We multiply parentheses

-18n-(8n(3n+7))+9+9=0


We calculate terms in parentheses: -(8n(3n+7)), so:

8n(3n+7)

We multiply parentheses

24n^2+56n

Back to the equation:

-(24n^2+56n)


We add all the numbers together, and all the variables

-18n-(24n^2+56n)+18=0

We get rid of parentheses

-24n^2-18n-56n+18=0

We add all the numbers together, and all the variables

-24n^2-74n+18=0

a = -24; b = -74; c = +18;
Δ = b2-4ac
Δ = -742-4·(-24)·18
Δ = 7204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7204}=\sqrt{4*1801}=\sqrt{4}*\sqrt{1801}=2\sqrt{1801}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{1801}}{2*-24}=\frac{74-2\sqrt{1801}}{-48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{1801}}{2*-24}=\frac{74+2\sqrt{1801}}{-48}
$