-2(1-7n)5n=34

Solution for -2(1-7n)5n=34 equation:

-2(1-7n)5n=34

We move all terms to the left:

-2(1-7n)5n-(34)=0

We add all the numbers together, and all the variables

-2(-7n+1)5n-34=0

We multiply parentheses

70n^2-10n-34=0

a = 70; b = -10; c = -34;
Δ = b2-4ac
Δ = -102-4·70·(-34)
Δ = 9620
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:

$\sqrt{\Delta}=\sqrt{9620}=\sqrt{4*2405}=\sqrt{4}*\sqrt{2405}=2\sqrt{2405}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{2405}}{2*70}=\frac{10-2\sqrt{2405}}{140}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{2405}}{2*70}=\frac{10+2\sqrt{2405}}{140}
$