8-3/2x+6=-94/3x-8

Solution for 8-3/2x+6=-94/3x-8 equation:

8-3/2x+6=-94/3x-8

We move all terms to the left:

8-3/2x+6-(-94/3x-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-8)!=0

x∈R


We add all the numbers together, and all the variables

-3/2x-(-94/3x-8)+14=0

We get rid of parentheses

-3/2x+94/3x+8+14=0

We calculate fractions


(-9x)/6x^2+188x/6x^2+8+14=0

We add all the numbers together, and all the variables

(-9x)/6x^2+188x/6x^2+22=0

We multiply all the terms by the denominator


(-9x)+188x+22*6x^2=0

We add all the numbers together, and all the variables

188x+(-9x)+22*6x^2=0

Wy multiply elements

132x^2+188x+(-9x)=0

We get rid of parentheses

132x^2+188x-9x=0

We add all the numbers together, and all the variables

132x^2+179x=0

a = 132; b = 179; c = 0;
Δ = b2-4ac
Δ = 1792-4·132·0
Δ = 32041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32041}=179$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(179)-179}{2*132}=\frac{-358}{264}
=-1+47/132
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(179)+179}{2*132}=\frac{0}{264}
=0
$