10(3/5n+4)=10(3/10n+7)

Solution for 10(3/5n+4)=10(3/10n+7) equation:

10(3/5n+4)=10(3/10n+7)

We move all terms to the left:

10(3/5n+4)-(10(3/10n+7))=0


Domain of the equation: 5n+4)!=0

n∈R



Domain of the equation: 10n+7))!=0

n∈R


We multiply parentheses

30n-(10(3/10n+7))+40=0

We multiply all the terms by the denominator


30n*10n+40*10n+7))-(10(3+7))=0

We add all the numbers together, and all the variables

30n*10n+40*10n+7))-(1010)=0

We add all the numbers together, and all the variables

30n*10n+40*10n=0

Wy multiply elements

300n^2+400n=0

a = 300; b = 400; c = 0;
Δ = b2-4ac
Δ = 4002-4·300·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-400}{2*300}=\frac{-800}{600}
=-1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+400}{2*300}=\frac{0}{600}
=0
$