(1/4)(n+5)=16

Solution for (1/4)(n+5)=16 equation:

(1/4)(n+5)=16

We move all terms to the left:

(1/4)(n+5)-(16)=0


Domain of the equation: 4)(n+5)!=0

n∈R


We add all the numbers together, and all the variables

(+1/4)(n+5)-16=0

We multiply parentheses ..

(+n^2+1/4*5)-16=0

We multiply all the terms by the denominator


(+n^2+1-16*4*5)=0

We get rid of parentheses

n^2+1-16*4*5=0

We add all the numbers together, and all the variables

n^2-319=0

a = 1; b = 0; c = -319;
Δ = b2-4ac
Δ = 02-4·1·(-319)
Δ = 1276
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:

$\sqrt{\Delta}=\sqrt{1276}=\sqrt{4*319}=\sqrt{4}*\sqrt{319}=2\sqrt{319}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{319}}{2*1}=\frac{0-2\sqrt{319}}{2}
=-\frac{2\sqrt{319}}{2}
=-\sqrt{319}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{319}}{2*1}=\frac{0+2\sqrt{319}}{2}
=\frac{2\sqrt{319}}{2}
=\sqrt{319}
$