4n^2-55=-9n

Solution for 4n^2-55=-9n equation:

4n^2-55=-9n

We move all terms to the left:

4n^2-55-(-9n)=0

We get rid of parentheses

4n^2+9n-55=0

a = 4; b = 9; c = -55;
Δ = b2-4ac
Δ = 92-4·4·(-55)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-31}{2*4}=\frac{-40}{8}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+31}{2*4}=\frac{22}{8}
=2+3/4
$