2x+5/3x=30

Solution for 2x+5/3x=30 equation:

2x+5/3x=30

We move all terms to the left:

2x+5/3x-(30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-30*3x+5=0

Wy multiply elements

6x^2-90x+5=0

a = 6; b = -90; c = +5;
Δ = b2-4ac
Δ = -902-4·6·5
Δ = 7980
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:

$\sqrt{\Delta}=\sqrt{7980}=\sqrt{4*1995}=\sqrt{4}*\sqrt{1995}=2\sqrt{1995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1995}}{2*6}=\frac{90-2\sqrt{1995}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1995}}{2*6}=\frac{90+2\sqrt{1995}}{12}
$