5x-3/3x=2

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

5x-3/3x=2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

15x^2-6x-3=0

a = 15; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·15·(-3)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{6}}{2*15}=\frac{6-6\sqrt{6}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{6}}{2*15}=\frac{6+6\sqrt{6}}{30}
$