2+n=7/8n-15

Solution for 2+n=7/8n-15 equation:

2+n=7/8n-15

We move all terms to the left:

2+n-(7/8n-15)=0


Domain of the equation: 8n-15)!=0

n∈R


We get rid of parentheses

n-7/8n+15+2=0

We multiply all the terms by the denominator


n*8n+15*8n+2*8n-7=0

Wy multiply elements

8n^2+120n+16n-7=0

We add all the numbers together, and all the variables

8n^2+136n-7=0

a = 8; b = 136; c = -7;
Δ = b2-4ac
Δ = 1362-4·8·(-7)
Δ = 18720
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:

$\sqrt{\Delta}=\sqrt{18720}=\sqrt{144*130}=\sqrt{144}*\sqrt{130}=12\sqrt{130}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-12\sqrt{130}}{2*8}=\frac{-136-12\sqrt{130}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+12\sqrt{130}}{2*8}=\frac{-136+12\sqrt{130}}{16}
$