7n(34-2n)+(2+3n)=60

Solution for 7n(34-2n)+(2+3n)=60 equation:

7n(34-2n)+(2+3n)=60

We move all terms to the left:

7n(34-2n)+(2+3n)-(60)=0

We add all the numbers together, and all the variables

7n(-2n+34)+(3n+2)-60=0

We multiply parentheses

-14n^2+238n+(3n+2)-60=0

We get rid of parentheses

-14n^2+238n+3n+2-60=0

We add all the numbers together, and all the variables

-14n^2+241n-58=0

a = -14; b = 241; c = -58;
Δ = b2-4ac
Δ = 2412-4·(-14)·(-58)
Δ = 54833
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{-(241)-\sqrt{54833}}{2*-14}=\frac{-241-\sqrt{54833}}{-28}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(241)+\sqrt{54833}}{2*-14}=\frac{-241+\sqrt{54833}}{-28}
$