24=x+3/5x

Solution for 24=x+3/5x equation:

24=x+3/5x

We move all terms to the left:

24-(x+3/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+3/5x)+24=0

We get rid of parentheses

-x-3/5x+24=0

We multiply all the terms by the denominator


-x*5x+24*5x-3=0

Wy multiply elements

-5x^2+120x-3=0

a = -5; b = 120; c = -3;
Δ = b2-4ac
Δ = 1202-4·(-5)·(-3)
Δ = 14340
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:

$\sqrt{\Delta}=\sqrt{14340}=\sqrt{4*3585}=\sqrt{4}*\sqrt{3585}=2\sqrt{3585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3585}}{2*-5}=\frac{-120-2\sqrt{3585}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3585}}{2*-5}=\frac{-120+2\sqrt{3585}}{-10}
$