(5/6)n=175

Solution for (5/6)n=175 equation:

(5/6)n=175

We move all terms to the left:

(5/6)n-(175)=0


Domain of the equation: 6)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+5/6)n-175=0

We multiply parentheses

5n^2-175=0

a = 5; b = 0; c = -175;
Δ = b2-4ac
Δ = 02-4·5·(-175)
Δ = 3500
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:

$\sqrt{\Delta}=\sqrt{3500}=\sqrt{100*35}=\sqrt{100}*\sqrt{35}=10\sqrt{35}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{35}}{2*5}=\frac{0-10\sqrt{35}}{10}
=-\frac{10\sqrt{35}}{10}
=-\sqrt{35}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{35}}{2*5}=\frac{0+10\sqrt{35}}{10}
=\frac{10\sqrt{35}}{10}
=\sqrt{35}
$