x+3/5x=24

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

x+3/5x=24

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


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}
$