4n^2-36n=-56

Solution for 4n^2-36n=-56 equation:

4n^2-36n=-56

We move all terms to the left:

4n^2-36n-(-56)=0

We add all the numbers together, and all the variables

4n^2-36n+56=0

a = 4; b = -36; c = +56;
Δ = b2-4ac
Δ = -362-4·4·56
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-20}{2*4}=\frac{16}{8}
=2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+20}{2*4}=\frac{56}{8}
=7
$