0.36n(100n+5)=0.6(30n+15)

Solution for 0.36n(100n+5)=0.6(30n+15) equation:

0.36n(100n+5)=0.6(30n+15)

We move all terms to the left:

0.36n(100n+5)-(0.6(30n+15))=0

We multiply parentheses

0n^2+0n-(0.6(30n+15))=0


We calculate terms in parentheses: -(0.6(30n+15)), so:

0.6(30n+15)

We multiply parentheses

18n+9

Back to the equation:

-(18n+9)


We add all the numbers together, and all the variables

n^2+n-(18n+9)=0

We get rid of parentheses

n^2+n-18n-9=0

We add all the numbers together, and all the variables

n^2-17n-9=0

a = 1; b = -17; c = -9;
Δ = b2-4ac
Δ = -172-4·1·(-9)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-5\sqrt{13}}{2*1}=\frac{17-5\sqrt{13}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+5\sqrt{13}}{2*1}=\frac{17+5\sqrt{13}}{2}
$