(-3/4)n+5=1

Solution for (-3/4)n+5=1 equation:

(-3/4)n+5=1

We move all terms to the left:

(-3/4)n+5-(1)=0


Domain of the equation: 4)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(-3/4)n+4=0

We multiply parentheses

-3n^2+4=0

a = -3; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-3)·4
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-3}=\frac{0-4\sqrt{3}}{-6}
=-\frac{4\sqrt{3}}{-6}
=-\frac{2\sqrt{3}}{-3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-3}=\frac{0+4\sqrt{3}}{-6}
=\frac{4\sqrt{3}}{-6}
=\frac{2\sqrt{3}}{-3}
$