(3/5)(n+12.6)=21

Solution for (3/5)(n+12.6)=21 equation:

(3/5)(n+12.6)=21

We move all terms to the left:

(3/5)(n+12.6)-(21)=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)-21=0

We multiply parentheses ..

(+3n^2+3/5*12.6)-21=0

We multiply all the terms by the denominator


(+3n^2+3-21*5*12.6)=0

We get rid of parentheses

3n^2+3-21*5*12.6=0

We add all the numbers together, and all the variables

3n^2-1320=0

a = 3; b = 0; c = -1320;
Δ = b2-4ac
Δ = 02-4·3·(-1320)
Δ = 15840
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:

$\sqrt{\Delta}=\sqrt{15840}=\sqrt{144*110}=\sqrt{144}*\sqrt{110}=12\sqrt{110}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{110}}{2*3}=\frac{0-12\sqrt{110}}{6}
=-\frac{12\sqrt{110}}{6}
=-2\sqrt{110}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{110}}{2*3}=\frac{0+12\sqrt{110}}{6}
=\frac{12\sqrt{110}}{6}
=2\sqrt{110}
$