7/10n+3/2=3/2n+2

Solution for 7/10n+3/2=3/2n+2 equation:

7/10n+3/2=3/2n+2

We move all terms to the left:

7/10n+3/2-(3/2n+2)=0


Domain of the equation: 10n!=0

n!=0/10

n!=0

n∈R



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

n∈R


We get rid of parentheses

7/10n-3/2n-2+3/2=0

We calculate fractions


56n/80n^2+(-30n)/80n^2+30n/80n^2-2=0

We multiply all the terms by the denominator


56n+(-30n)+30n-2*80n^2=0

We add all the numbers together, and all the variables

86n+(-30n)-2*80n^2=0

Wy multiply elements

-160n^2+86n+(-30n)=0

We get rid of parentheses

-160n^2+86n-30n=0

We add all the numbers together, and all the variables

-160n^2+56n=0

a = -160; b = 56; c = 0;
Δ = b2-4ac
Δ = 562-4·(-160)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-56}{2*-160}=\frac{-112}{-320}
=7/20
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+56}{2*-160}=\frac{0}{-320}
=0
$