/4n-20=6n+10

Solution for /4n-20=6n+10 equation:

/4n-20=6n+10

We move all terms to the left:

/4n-20-(6n+10)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We get rid of parentheses

/4n-6n-10-20=0

We multiply all the terms by the denominator


-6n*4n-10*4n-20*4n+=0

We add all the numbers together, and all the variables

-6n*4n-10*4n-20*4n=0

Wy multiply elements

-24n^2-40n-80n=0

We add all the numbers together, and all the variables

-24n^2-120n=0

a = -24; b = -120; c = 0;
Δ = b2-4ac
Δ = -1202-4·(-24)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120}{2*-24}=\frac{0}{-48}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120}{2*-24}=\frac{240}{-48}
=-5
$