4n^2-52n+144=0

Solution for 4n^2-52n+144=0 equation:

4n^2-52n+144=0

a = 4; b = -52; c = +144;
Δ = b2-4ac
Δ = -522-4·4·144
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-20}{2*4}=\frac{32}{8}
=4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+20}{2*4}=\frac{72}{8}
=9
$