/4n+5=6n+8*

Solution for /4n+5=6n+8* equation:

/4n+5=6n+8*

We move all terms to the left:

/4n+5-(6n+8*)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

/4n-(+6n)+5=0

We get rid of parentheses

/4n-6n+5=0

We multiply all the terms by the denominator


-6n*4n+5*4n+=0

We add all the numbers together, and all the variables

-6n*4n+5*4n=0

Wy multiply elements

-24n^2+20n=0

a = -24; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-24)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-24}=\frac{-40}{-48}
=5/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-24}=\frac{0}{-48}
=0
$