-1/2n+-3/4n=-7/16

Solution for -1/2n+-3/4n=-7/16 equation:

-1/2n+-3/4n=-7/16

We move all terms to the left:

-1/2n+-3/4n-(-7/16)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

-1/2n-3/4n-(-7/16)=0

We get rid of parentheses

-1/2n-3/4n+7/16=0

We calculate fractions


224n^2/128n^2+(-64n)/128n^2+(-96n)/128n^2=0

We multiply all the terms by the denominator


224n^2+(-64n)+(-96n)=0

We get rid of parentheses

224n^2-64n-96n=0

We add all the numbers together, and all the variables

224n^2-160n=0

a = 224; b = -160; c = 0;
Δ = b2-4ac
Δ = -1602-4·224·0
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-160}{2*224}=\frac{0}{448}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+160}{2*224}=\frac{320}{448}
=5/7
$