n(3n-1)+4n=26

Solution for n(3n-1)+4n=26 equation:

n(3n-1)+4n=26

We move all terms to the left:

n(3n-1)+4n-(26)=0

We add all the numbers together, and all the variables

4n+n(3n-1)-26=0

We multiply parentheses

3n^2+4n-1n-26=0

We add all the numbers together, and all the variables

3n^2+3n-26=0

a = 3; b = 3; c = -26;
Δ = b2-4ac
Δ = 32-4·3·(-26)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{321}}{2*3}=\frac{-3-\sqrt{321}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{321}}{2*3}=\frac{-3+\sqrt{321}}{6}
$