5x+2/3x=4

Solution for 5x+2/3x=4 equation:

5x+2/3x=4

We move all terms to the left:

5x+2/3x-(4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


5x*3x-4*3x+2=0

Wy multiply elements

15x^2-12x+2=0

a = 15; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·15·2
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{6}}{2*15}=\frac{12-2\sqrt{6}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{6}}{2*15}=\frac{12+2\sqrt{6}}{30}
$