(5x-7/3x)=2

Solution for (5x-7/3x)=2 equation:

(5x-7/3x)=2

We move all terms to the left:

(5x-7/3x)-(2)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5x-7/3x)-2=0

We get rid of parentheses

5x-7/3x-2=0

We multiply all the terms by the denominator


5x*3x-2*3x-7=0

Wy multiply elements

15x^2-6x-7=0

a = 15; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·15·(-7)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{114}}{2*15}=\frac{6-2\sqrt{114}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{114}}{2*15}=\frac{6+2\sqrt{114}}{30}
$