N/6n-4=3n+24

Solution for N/6n-4=3n+24 equation:

/6N-4=3N+24

We move all terms to the left:

/6N-4-(3N+24)=0


Domain of the equation: 6N!=0

N!=0/6

N!=0

N∈R


We get rid of parentheses

/6N-3N-24-4=0

We multiply all the terms by the denominator


-3N*6N-24*6N-4*6N+=0

We add all the numbers together, and all the variables

-3N*6N-24*6N-4*6N=0

Wy multiply elements

-18N^2-144N-24N=0

We add all the numbers together, and all the variables

-18N^2-168N=0

a = -18; b = -168; c = 0;
Δ = b2-4ac
Δ = -1682-4·(-18)·0
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-168}{2*-18}=\frac{0}{-36}
=0
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+168}{2*-18}=\frac{336}{-36}
=-9+1/3
$