(3/5)(n+12.6)=22

Solution for (3/5)(n+12.6)=22 equation:

(3/5)(n+12.6)=22

We move all terms to the left:

(3/5)(n+12.6)-(22)=0


Domain of the equation: 5)(n+12.6)!=0

n∈R


We add all the numbers together, and all the variables

(+3/5)(n+12.6)-22=0

We multiply parentheses ..

(+3n^2+3/5*12.6)-22=0

We multiply all the terms by the denominator


(+3n^2+3-22*5*12.6)=0

We get rid of parentheses

3n^2+3-22*5*12.6=0

We add all the numbers together, and all the variables

3n^2-1383=0

a = 3; b = 0; c = -1383;
Δ = b2-4ac
Δ = 02-4·3·(-1383)
Δ = 16596
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:

$\sqrt{\Delta}=\sqrt{16596}=\sqrt{36*461}=\sqrt{36}*\sqrt{461}=6\sqrt{461}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{461}}{2*3}=\frac{0-6\sqrt{461}}{6}
=-\frac{6\sqrt{461}}{6}
=-\sqrt{461}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{461}}{2*3}=\frac{0+6\sqrt{461}}{6}
=\frac{6\sqrt{461}}{6}
=\sqrt{461}
$