4n^2+5=9n

Solution for 4n^2+5=9n equation:

4n^2+5=9n

We move all terms to the left:

4n^2+5-(9n)=0

a = 4; b = -9; c = +5;
Δ = b2-4ac
Δ = -92-4·4·5
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*4}=\frac{8}{8}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*4}=\frac{10}{8}
=1+1/4
$