8=-18+(3/8)(16-30n)

Solution for 8=-18+(3/8)(16-30n) equation:

8=-18+(3/8)(16-30n)

We move all terms to the left:

8-(-18+(3/8)(16-30n))=0


Domain of the equation: 8)(16-30n))!=0

n∈R


We add all the numbers together, and all the variables

-(-18+(+3/8)(-30n+16))+8=0

We multiply parentheses ..

-(-18+(-90n^2+3/8*16))+8=0

We multiply all the terms by the denominator


-(-18+(-90n^2+3+8*8*16))=0


We calculate terms in parentheses: -(-18+(-90n^2+3+8*8*16)), so:

-18+(-90n^2+3+8*8*16)

determiningTheFunctionDomain
(-90n^2+3+8*8*16)-18

We get rid of parentheses

-90n^2+3-18+8*8*16

We add all the numbers together, and all the variables

-90n^2+1009

Back to the equation:

-(-90n^2+1009)


We get rid of parentheses

90n^2-1009=0

a = 90; b = 0; c = -1009;
Δ = b2-4ac
Δ = 02-4·90·(-1009)
Δ = 363240
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:

$\sqrt{\Delta}=\sqrt{363240}=\sqrt{36*10090}=\sqrt{36}*\sqrt{10090}=6\sqrt{10090}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10090}}{2*90}=\frac{0-6\sqrt{10090}}{180}
=-\frac{6\sqrt{10090}}{180}
=-\frac{\sqrt{10090}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10090}}{2*90}=\frac{0+6\sqrt{10090}}{180}
=\frac{6\sqrt{10090}}{180}
=\frac{\sqrt{10090}}{30}
$