5x=12/x=-24

Solution for 5x=12/x=-24 equation:

5x=12/x=-24

We move all terms to the left:

5x-(12/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+12/x)=0

We get rid of parentheses

5x-12/x=0

We multiply all the terms by the denominator


5x*x-12=0

Wy multiply elements

5x^2-12=0

a = 5; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·5·(-12)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*5}=\frac{0-4\sqrt{15}}{10}
=-\frac{4\sqrt{15}}{10}
=-\frac{2\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*5}=\frac{0+4\sqrt{15}}{10}
=\frac{4\sqrt{15}}{10}
=\frac{2\sqrt{15}}{5}
$