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

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

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

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n-10)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

120n^2+4n-6n=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{0}{240}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*120}=\frac{4}{240}
=1/60
$