n+5n(n-1)=7

Solution for n+5n(n-1)=7 equation:

n+5n(n-1)=7

We move all terms to the left:

n+5n(n-1)-(7)=0

We multiply parentheses

5n^2+n-5n-7=0

We add all the numbers together, and all the variables

5n^2-4n-7=0

a = 5; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·5·(-7)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{39}}{2*5}=\frac{4-2\sqrt{39}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{39}}{2*5}=\frac{4+2\sqrt{39}}{10}
$