30n^2+34(n-1)+1,n=4

Solution for 30n^2+34(n-1)+1,n=4 equation:

30n^2+34(n-1)+1.n=4

We move all terms to the left:

30n^2+34(n-1)+1.n-(4)=0

We add all the numbers together, and all the variables

30n^2+n+34(n-1)-4=0

We multiply parentheses

30n^2+n+34n-34-4=0

We add all the numbers together, and all the variables

30n^2+35n-38=0

a = 30; b = 35; c = -38;
Δ = b2-4ac
Δ = 352-4·30·(-38)
Δ = 5785
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{-(35)-\sqrt{5785}}{2*30}=\frac{-35-\sqrt{5785}}{60}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{5785}}{2*30}=\frac{-35+\sqrt{5785}}{60}
$