2n^2-39=-7n

Solution for 2n^2-39=-7n equation:

2n^2-39=-7n

We move all terms to the left:

2n^2-39-(-7n)=0

We get rid of parentheses

2n^2+7n-39=0

a = 2; b = 7; c = -39;
Δ = b2-4ac
Δ = 72-4·2·(-39)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-19}{2*2}=\frac{-26}{4}
=-6+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+19}{2*2}=\frac{12}{4}
=3
$