8n+3=15/8n

Solution for 8n+3=15/8n equation:

8n+3=15/8n

We move all terms to the left:

8n+3-(15/8n)=0


Domain of the equation: 8n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

8n-(+15/8n)+3=0

We get rid of parentheses

8n-15/8n+3=0

We multiply all the terms by the denominator


8n*8n+3*8n-15=0

Wy multiply elements

64n^2+24n-15=0

a = 64; b = 24; c = -15;
Δ = b2-4ac
Δ = 242-4·64·(-15)
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{69}}{2*64}=\frac{-24-8\sqrt{69}}{128}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{69}}{2*64}=\frac{-24+8\sqrt{69}}{128}
$