7n^2+12=44n

Solution for 7n^2+12=44n equation:

7n^2+12=44n

We move all terms to the left:

7n^2+12-(44n)=0

a = 7; b = -44; c = +12;
Δ = b2-4ac
Δ = -442-4·7·12
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-40}{2*7}=\frac{4}{14}
=2/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+40}{2*7}=\frac{84}{14}
=6
$