5n^2-24n+21=5

Solution for 5n^2-24n+21=5 equation:

5n^2-24n+21=5

We move all terms to the left:

5n^2-24n+21-(5)=0

We add all the numbers together, and all the variables

5n^2-24n+16=0

a = 5; b = -24; c = +16;
Δ = b2-4ac
Δ = -242-4·5·16
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16}{2*5}=\frac{8}{10}
=4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16}{2*5}=\frac{40}{10}
=4
$