4n^2-12=5n

Solution for 4n^2-12=5n equation:

4n^2-12=5n

We move all terms to the left:

4n^2-12-(5n)=0

a = 4; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·4·(-12)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{217}}{2*4}=\frac{5-\sqrt{217}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*4}=\frac{5+\sqrt{217}}{8}
$