(6n+5)4n-5=180

Solution for (6n+5)4n-5=180 equation:

(6n+5)4n-5=180

We move all terms to the left:

(6n+5)4n-5-(180)=0

We add all the numbers together, and all the variables

(6n+5)4n-185=0

We multiply parentheses

24n^2+20n-185=0

a = 24; b = 20; c = -185;
Δ = b2-4ac
Δ = 202-4·24·(-185)
Δ = 18160
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:

$\sqrt{\Delta}=\sqrt{18160}=\sqrt{16*1135}=\sqrt{16}*\sqrt{1135}=4\sqrt{1135}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{1135}}{2*24}=\frac{-20-4\sqrt{1135}}{48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{1135}}{2*24}=\frac{-20+4\sqrt{1135}}{48}
$