2x+5/3x-1=-5

Solution for 2x+5/3x-1=-5 equation:

2x+5/3x-1=-5

We move all terms to the left:

2x+5/3x-1-(-5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+5/3x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+12x+5=0

a = 6; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·6·5
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*6}=\frac{-12-2\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{6}}{2*6}=\frac{-12+2\sqrt{6}}{12}
$