8/x+1-1/2=4/3x+3

Solution for 8/x+1-1/2=4/3x+3 equation:

8/x+1-1/2=4/3x+3

We move all terms to the left:

8/x+1-1/2-(4/3x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+3)!=0

x∈R


We get rid of parentheses

8/x-4/3x-3+1-1/2=0

We calculate fractions


(-9x^2)/12x^2+96x/12x^2+(-16x)/12x^2-3+1=0

We add all the numbers together, and all the variables

(-9x^2)/12x^2+96x/12x^2+(-16x)/12x^2-2=0

We multiply all the terms by the denominator


(-9x^2)+96x+(-16x)-2*12x^2=0

Wy multiply elements

(-9x^2)-24x^2+96x+(-16x)=0

We get rid of parentheses

-9x^2-24x^2+96x-16x=0

We add all the numbers together, and all the variables

-33x^2+80x=0

a = -33; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-33)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*-33}=\frac{-160}{-66}
=2+14/33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-33}=\frac{0}{-66}
=0
$