65/3x+14=13/2x

Solution for 65/3x+14=13/2x equation:

65/3x+14=13/2x

We move all terms to the left:

65/3x+14-(13/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

65/3x-(+13/2x)+14=0

We get rid of parentheses

65/3x-13/2x+14=0

We calculate fractions


130x/6x^2+(-39x)/6x^2+14=0

We multiply all the terms by the denominator


130x+(-39x)+14*6x^2=0

Wy multiply elements

84x^2+130x+(-39x)=0

We get rid of parentheses

84x^2+130x-39x=0

We add all the numbers together, and all the variables

84x^2+91x=0

a = 84; b = 91; c = 0;
Δ = b2-4ac
Δ = 912-4·84·0
Δ = 8281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8281}=91$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-91}{2*84}=\frac{-182}{168}
=-1+1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+91}{2*84}=\frac{0}{168}
=0
$