3/4n-10=1/2n+5

Solution for 3/4n-10=1/2n+5 equation:

3/4n-10=1/2n+5

We move all terms to the left:

3/4n-10-(1/2n+5)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n+5)!=0

n∈R


We get rid of parentheses

3/4n-1/2n-5-10=0

We calculate fractions


6n/8n^2+(-4n)/8n^2-5-10=0

We add all the numbers together, and all the variables

6n/8n^2+(-4n)/8n^2-15=0

We multiply all the terms by the denominator


6n+(-4n)-15*8n^2=0

Wy multiply elements

-120n^2+6n+(-4n)=0

We get rid of parentheses

-120n^2+6n-4n=0

We add all the numbers together, and all the variables

-120n^2+2n=0

a = -120; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-120)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-120}=\frac{-4}{-240}
=1/60
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-120}=\frac{0}{-240}
=0
$