13/6x=3/2x+1

Solution for 13/6x=3/2x+1 equation:

13/6x=3/2x+1

We move all terms to the left:

13/6x-(3/2x+1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

13/6x-3/2x-1=0

We calculate fractions


26x/12x^2+(-18x)/12x^2-1=0

We multiply all the terms by the denominator


26x+(-18x)-1*12x^2=0

Wy multiply elements

-12x^2+26x+(-18x)=0

We get rid of parentheses

-12x^2+26x-18x=0

We add all the numbers together, and all the variables

-12x^2+8x=0

a = -12; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-12)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-12}=\frac{-16}{-24}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-12}=\frac{0}{-24}
=0
$