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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3n+20n-(3n(4n-9))+28=0


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

3n(4n-9)

We multiply parentheses

12n^2-27n

Back to the equation:

-(12n^2-27n)


We add all the numbers together, and all the variables

17n-(12n^2-27n)+28=0

We get rid of parentheses

-12n^2+17n+27n+28=0

We add all the numbers together, and all the variables

-12n^2+44n+28=0

a = -12; b = 44; c = +28;
Δ = b2-4ac
Δ = 442-4·(-12)·28
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{205}}{2*-12}=\frac{-44-4\sqrt{205}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{205}}{2*-12}=\frac{-44+4\sqrt{205}}{-24}
$