x-5/3x-3=-1

Solution for x-5/3x-3=-1 equation:

x-5/3x-3=-1

We move all terms to the left:

x-5/3x-3-(-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x-5/3x-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-6x-5=0

a = 3; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·3·(-5)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*3}=\frac{6-4\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*3}=\frac{6+4\sqrt{6}}{6}
$