5/6x-4=3/2x+1

Solution for 5/6x-4=3/2x+1 equation:

5/6x-4=3/2x+1

We move all terms to the left:

5/6x-4-(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

5/6x-3/2x-1-4=0

We calculate fractions


10x/12x^2+(-18x)/12x^2-1-4=0

We add all the numbers together, and all the variables

10x/12x^2+(-18x)/12x^2-5=0

We multiply all the terms by the denominator


10x+(-18x)-5*12x^2=0

Wy multiply elements

-60x^2+10x+(-18x)=0

We get rid of parentheses

-60x^2+10x-18x=0

We add all the numbers together, and all the variables

-60x^2-8x=0

a = -60; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-60)·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*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-60}=\frac{16}{-120}
=-2/15
$