(4/9)(36-18n)=-8

Solution for (4/9)(36-18n)=-8 equation:

(4/9)(36-18n)=-8

We move all terms to the left:

(4/9)(36-18n)-(-8)=0


Domain of the equation: 9)(36-18n)!=0

n∈R


We add all the numbers together, and all the variables

(+4/9)(-18n+36)-(-8)=0

We add all the numbers together, and all the variables

(+4/9)(-18n+36)+8=0

We multiply parentheses ..

(-72n^2+4/9*36)+8=0

We multiply all the terms by the denominator


(-72n^2+4+8*9*36)=0

We get rid of parentheses

-72n^2+4+8*9*36=0

We add all the numbers together, and all the variables

-72n^2+2596=0

a = -72; b = 0; c = +2596;
Δ = b2-4ac
Δ = 02-4·(-72)·2596
Δ = 747648
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:

$\sqrt{\Delta}=\sqrt{747648}=\sqrt{576*1298}=\sqrt{576}*\sqrt{1298}=24\sqrt{1298}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{1298}}{2*-72}=\frac{0-24\sqrt{1298}}{-144}
=-\frac{24\sqrt{1298}}{-144}
=-\frac{\sqrt{1298}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{1298}}{2*-72}=\frac{0+24\sqrt{1298}}{-144}
=\frac{24\sqrt{1298}}{-144}
=\frac{\sqrt{1298}}{-6}
$