-19/x^-2-72x+4320=0

Solution for -19/x^-2-72x+4320=0 equation:

-19/x^-2-72x+4320=0


Domain of the equation: x^!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-72x-19/x^+4318=0

We multiply all the terms by the denominator


-72x*x^+4318*x^-19=0

We add all the numbers together, and all the variables

4318x-72x*x^-19=0

Wy multiply elements

-72x^2+4318x-19=0

a = -72; b = 4318; c = -19;
Δ = b2-4ac
Δ = 43182-4·(-72)·(-19)
Δ = 18639652
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18639652}=\sqrt{4*4659913}=\sqrt{4}*\sqrt{4659913}=2\sqrt{4659913}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4318)-2\sqrt{4659913}}{2*-72}=\frac{-4318-2\sqrt{4659913}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4318)+2\sqrt{4659913}}{2*-72}=\frac{-4318+2\sqrt{4659913}}{-144}
$