((1)/((4)))n-3=25

Solution for ((1)/((4)))n-3=25 equation:

((1)/((4)))n-3=25

We move all terms to the left:

((1)/((4)))n-3-(25)=0


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

n∈R


determiningTheFunctionDomain
(1/4)n-3-25=0

We add all the numbers together, and all the variables

(+1/4)n-3-25=0

We add all the numbers together, and all the variables

(+1/4)n-28=0

We multiply parentheses

n^2-28=0

a = 1; b = 0; c = -28;
Δ = b2-4ac
Δ = 02-4·1·(-28)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*1}=\frac{0-4\sqrt{7}}{2}
=-\frac{4\sqrt{7}}{2}
=-2\sqrt{7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*1}=\frac{0+4\sqrt{7}}{2}
=\frac{4\sqrt{7}}{2}
=2\sqrt{7}
$