3/2x-8=5/6x+2

Solution for 3/2x-8=5/6x+2 equation:

3/2x-8=5/6x+2

We move all terms to the left:

3/2x-8-(5/6x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+2)!=0

x∈R


We get rid of parentheses

3/2x-5/6x-2-8=0

We calculate fractions


18x/12x^2+(-10x)/12x^2-2-8=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-120x^2+18x+(-10x)=0

We get rid of parentheses

-120x^2+18x-10x=0

We add all the numbers together, and all the variables

-120x^2+8x=0

a = -120; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-120)·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*-120}=\frac{-16}{-240}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-120}=\frac{0}{-240}
=0
$