6(n+5)=3(n+16)6n+5=3(n+16)

Solution for 6(n+5)=3(n+16)6n+5=3(n+16) equation:

6(n+5)=3(n+16)6n+5=3(n+16)

We move all terms to the left:

6(n+5)-(3(n+16)6n+5)=0

We multiply parentheses

6n-(3(n+16)6n+5)+30=0


We calculate terms in parentheses: -(3(n+16)6n+5), so:

3(n+16)6n+5

We multiply parentheses

18n^2+288n+5

Back to the equation:

-(18n^2+288n+5)


We get rid of parentheses

-18n^2+6n-288n-5+30=0

We add all the numbers together, and all the variables

-18n^2-282n+25=0

a = -18; b = -282; c = +25;
Δ = b2-4ac
Δ = -2822-4·(-18)·25
Δ = 81324
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:

$\sqrt{\Delta}=\sqrt{81324}=\sqrt{324*251}=\sqrt{324}*\sqrt{251}=18\sqrt{251}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-282)-18\sqrt{251}}{2*-18}=\frac{282-18\sqrt{251}}{-36}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-282)+18\sqrt{251}}{2*-18}=\frac{282+18\sqrt{251}}{-36}
$