6-3/2x=-8/3x-1

Solution for 6-3/2x=-8/3x-1 equation:

6-3/2x=-8/3x-1

We move all terms to the left:

6-3/2x-(-8/3x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

-3/2x+8/3x+1+6=0

We calculate fractions


(-9x)/6x^2+16x/6x^2+1+6=0

We add all the numbers together, and all the variables

(-9x)/6x^2+16x/6x^2+7=0

We multiply all the terms by the denominator


(-9x)+16x+7*6x^2=0

We add all the numbers together, and all the variables

16x+(-9x)+7*6x^2=0

Wy multiply elements

42x^2+16x+(-9x)=0

We get rid of parentheses

42x^2+16x-9x=0

We add all the numbers together, and all the variables

42x^2+7x=0

a = 42; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·42·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*42}=\frac{-14}{84}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*42}=\frac{0}{84}
=0
$