n/8n+9=6n+25*

Solution for n/8n+9=6n+25* equation:

n/8n+9=6n+25*

We move all terms to the left:

n/8n+9-(6n+25*)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R


We add all the numbers together, and all the variables

n/8n-(+6n)+9=0

We get rid of parentheses

n/8n-6n+9=0

We multiply all the terms by the denominator


n-6n*8n+9*8n=0

Wy multiply elements

-48n^2+n+72n=0

We add all the numbers together, and all the variables

-48n^2+73n=0

a = -48; b = 73; c = 0;
Δ = b2-4ac
Δ = 732-4·(-48)·0
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(73)-73}{2*-48}=\frac{-146}{-96}
=1+25/48
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(73)+73}{2*-48}=\frac{0}{-96}
=0
$