n^2/5n-24=0

Solution for n^2/5n-24=0 equation:

n^2/5n-24=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We multiply all the terms by the denominator


n^2-24*5n=0

Wy multiply elements

n^2-120n=0

a = 1; b = -120; c = 0;
Δ = b2-4ac
Δ = -1202-4·1·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120}{2*1}=\frac{0}{2}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120}{2*1}=\frac{240}{2}
=120
$