3(-6-7n)3n=-144

Solution for 3(-6-7n)3n=-144 equation:

3(-6-7n)3n=-144

We move all terms to the left:

3(-6-7n)3n-(-144)=0

We add all the numbers together, and all the variables

3(-7n-6)3n-(-144)=0

We add all the numbers together, and all the variables

3(-7n-6)3n+144=0

We multiply parentheses

-63n^2-54n+144=0

a = -63; b = -54; c = +144;
Δ = b2-4ac
Δ = -542-4·(-63)·144
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39204}=198$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-198}{2*-63}=\frac{-144}{-126}
=1+1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+198}{2*-63}=\frac{252}{-126}
=-2
$