5x=2/3x+2

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

5x=2/3x+2

We move all terms to the left:

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


Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

5x-2/3x-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2-6x-2=0

a = 15; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·15·(-2)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*15}=\frac{6-2\sqrt{39}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*15}=\frac{6+2\sqrt{39}}{30}
$