4320/x-6x=0

Solution for 4320/x-6x=0 equation:

4320/x-6x=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6x+4320/x=0

We multiply all the terms by the denominator


-6x*x+4320=0

Wy multiply elements

-6x^2+4320=0

a = -6; b = 0; c = +4320;
Δ = b2-4ac
Δ = 02-4·(-6)·4320
Δ = 103680
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:

$\sqrt{\Delta}=\sqrt{103680}=\sqrt{20736*5}=\sqrt{20736}*\sqrt{5}=144\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{5}}{2*-6}=\frac{0-144\sqrt{5}}{-12}
=-\frac{144\sqrt{5}}{-12}
=-\frac{12\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{5}}{2*-6}=\frac{0+144\sqrt{5}}{-12}
=\frac{144\sqrt{5}}{-12}
=\frac{12\sqrt{5}}{-1}
$