5n^2-44=12n

Solution for 5n^2-44=12n equation:

5n^2-44=12n

We move all terms to the left:

5n^2-44-(12n)=0

a = 5; b = -12; c = -44;
Δ = b2-4ac
Δ = -122-4·5·(-44)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-32}{2*5}=\frac{-20}{10}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+32}{2*5}=\frac{44}{10}
=4+2/5
$