-3+5(n-3)7n=2

Solution for -3+5(n-3)7n=2 equation:

-3+5(n-3)7n=2

We move all terms to the left:

-3+5(n-3)7n-(2)=0

We add all the numbers together, and all the variables

5(n-3)7n-5=0

We multiply parentheses

35n^2-105n-5=0

a = 35; b = -105; c = -5;
Δ = b2-4ac
Δ = -1052-4·35·(-5)
Δ = 11725
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:

$\sqrt{\Delta}=\sqrt{11725}=\sqrt{25*469}=\sqrt{25}*\sqrt{469}=5\sqrt{469}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-5\sqrt{469}}{2*35}=\frac{105-5\sqrt{469}}{70}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+5\sqrt{469}}{2*35}=\frac{105+5\sqrt{469}}{70}
$