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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(-2n(-7n+1)), so:

-2n(-7n+1)

We multiply parentheses

14n^2-2n

Back to the equation:

-(14n^2-2n)


We get rid of parentheses

-14n^2+5n+2n+34=0

We add all the numbers together, and all the variables

-14n^2+7n+34=0

a = -14; b = 7; c = +34;
Δ = b2-4ac
Δ = 72-4·(-14)·34
Δ = 1953
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:

$\sqrt{\Delta}=\sqrt{1953}=\sqrt{9*217}=\sqrt{9}*\sqrt{217}=3\sqrt{217}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{217}}{2*-14}=\frac{-7-3\sqrt{217}}{-28}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{217}}{2*-14}=\frac{-7+3\sqrt{217}}{-28}
$