(5n+7)-3n=3(4n-9)n=-11

Solution for (5n+7)-3n=3(4n-9)n=-11 equation:

(5n+7)-3n=3(4n-9)n=-11

We move all terms to the left:

(5n+7)-3n-(3(4n-9)n)=0

We add all the numbers together, and all the variables

-3n+(5n+7)-(3(4n-9)n)=0

We get rid of parentheses

-3n+5n-(3(4n-9)n)+7=0


We calculate terms in parentheses: -(3(4n-9)n), so:

3(4n-9)n

We multiply parentheses

12n^2-27n

Back to the equation:

-(12n^2-27n)


We add all the numbers together, and all the variables

2n-(12n^2-27n)+7=0

We get rid of parentheses

-12n^2+2n+27n+7=0

We add all the numbers together, and all the variables

-12n^2+29n+7=0

a = -12; b = 29; c = +7;
Δ = b2-4ac
Δ = 292-4·(-12)·7
Δ = 1177
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{-(29)-\sqrt{1177}}{2*-12}=\frac{-29-\sqrt{1177}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{1177}}{2*-12}=\frac{-29+\sqrt{1177}}{-24}
$