-7n(n+3)=-34+6n

Solution for -7n(n+3)=-34+6n equation:

-7n(n+3)=-34+6n

We move all terms to the left:

-7n(n+3)-(-34+6n)=0

We add all the numbers together, and all the variables

-7n(n+3)-(6n-34)=0

We multiply parentheses

-7n^2-21n-(6n-34)=0

We get rid of parentheses

-7n^2-21n-6n+34=0

We add all the numbers together, and all the variables

-7n^2-27n+34=0

a = -7; b = -27; c = +34;
Δ = b2-4ac
Δ = -272-4·(-7)·34
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-41}{2*-7}=\frac{-14}{-14}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+41}{2*-7}=\frac{68}{-14}
=-4+6/7
$