1n+1.8=3/10n+22.8

Solution for 1n+1.8=3/10n+22.8 equation:

1n+1.8=3/10n+22.8

We move all terms to the left:

1n+1.8-(3/10n+22.8)=0


Domain of the equation: 10n+22.8)!=0

n∈R


We add all the numbers together, and all the variables

n-(3/10n+22.8)+1.8=0

We get rid of parentheses

n-3/10n-22.8+1.8=0

We multiply all the terms by the denominator


n*10n-(22.8)*10n+(1.8)*10n-3=0

We multiply parentheses

n*10n-228n+18n-3=0

Wy multiply elements

10n^2-228n+18n-3=0

We add all the numbers together, and all the variables

10n^2-210n-3=0

a = 10; b = -210; c = -3;
Δ = b2-4ac
Δ = -2102-4·10·(-3)
Δ = 44220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44220}=\sqrt{4*11055}=\sqrt{4}*\sqrt{11055}=2\sqrt{11055}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11055}}{2*10}=\frac{210-2\sqrt{11055}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11055}}{2*10}=\frac{210+2\sqrt{11055}}{20}
$