2n2+24=14n

Solution for 2n2+24=14n equation:

2n^2+24=14n

We move all terms to the left:

2n^2+24-(14n)=0

a = 2; b = -14; c = +24;
Δ = b2-4ac
Δ = -142-4·2·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2}{2*2}=\frac{12}{4}
=3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*2}=\frac{16}{4}
=4
$