0=2x+1/3x-5

Solution for 0=2x+1/3x-5 equation:

0=2x+1/3x-5

We move all terms to the left:

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


Domain of the equation: 3x-5)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*3x+5*3x-1=0

Wy multiply elements

-6x^2+15x-1=0

a = -6; b = 15; c = -1;
Δ = b2-4ac
Δ = 152-4·(-6)·(-1)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{201}}{2*-6}=\frac{-15-\sqrt{201}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{201}}{2*-6}=\frac{-15+\sqrt{201}}{-12}
$