(5/6)(n+1)=7

Solution for (5/6)(n+1)=7 equation:

(5/6)(n+1)=7

We move all terms to the left:

(5/6)(n+1)-(7)=0


Domain of the equation: 6)(n+1)!=0

n∈R


We add all the numbers together, and all the variables

(+5/6)(n+1)-7=0

We multiply parentheses ..

(+5n^2+5/6*1)-7=0

We multiply all the terms by the denominator


(+5n^2+5-7*6*1)=0

We get rid of parentheses

5n^2+5-7*6*1=0

We add all the numbers together, and all the variables

5n^2-37=0

a = 5; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·5·(-37)
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{185}}{2*5}=\frac{0-2\sqrt{185}}{10}
=-\frac{2\sqrt{185}}{10}
=-\frac{\sqrt{185}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{185}}{2*5}=\frac{0+2\sqrt{185}}{10}
=\frac{2\sqrt{185}}{10}
=\frac{\sqrt{185}}{5}
$