2/5n-2=7/10n-8

Solution for 2/5n-2=7/10n-8 equation:

2/5n-2=7/10n-8

We move all terms to the left:

2/5n-2-(7/10n-8)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 10n-8)!=0

n∈R


We get rid of parentheses

2/5n-7/10n+8-2=0

We calculate fractions


20n/50n^2+(-35n)/50n^2+8-2=0

We add all the numbers together, and all the variables

20n/50n^2+(-35n)/50n^2+6=0

We multiply all the terms by the denominator


20n+(-35n)+6*50n^2=0

Wy multiply elements

300n^2+20n+(-35n)=0

We get rid of parentheses

300n^2+20n-35n=0

We add all the numbers together, and all the variables

300n^2-15n=0

a = 300; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·300·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*300}=\frac{0}{600}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*300}=\frac{30}{600}
=1/20
$