n^2/5n-24=4

Solution for n^2/5n-24=4 equation:

n^2/5n-24=4

We move all terms to the left:

n^2/5n-24-(4)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

n^2/5n-28=0

We multiply all the terms by the denominator


n^2-28*5n=0

Wy multiply elements

n^2-140n=0

a = 1; b = -140; c = 0;
Δ = b2-4ac
Δ = -1402-4·1·0
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-140}{2*1}=\frac{0}{2}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+140}{2*1}=\frac{280}{2}
=140
$