5n^2+45=50n

Solution for 5n^2+45=50n equation:

5n^2+45=50n

We move all terms to the left:

5n^2+45-(50n)=0

a = 5; b = -50; c = +45;
Δ = b2-4ac
Δ = -502-4·5·45
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{-(-50)-40}{2*5}=\frac{10}{10}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+40}{2*5}=\frac{90}{10}
=9
$