-2n2+21n+44=-5-4n2

Solution for -2n2+21n+44=-5-4n2 equation:

-2n^2+21n+44=-5-4n^2

We move all terms to the left:

-2n^2+21n+44-(-5-4n^2)=0

We get rid of parentheses

-2n^2+4n^2+21n+5+44=0

We add all the numbers together, and all the variables

2n^2+21n+49=0

a = 2; b = 21; c = +49;
Δ = b2-4ac
Δ = 212-4·2·49
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-7}{2*2}=\frac{-28}{4}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+7}{2*2}=\frac{-14}{4}
=-3+1/2
$