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

Solution for 8/x+1-5/2=6/3x+3 equation:

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

We move all terms to the left:

8/x+1-5/2-(6/3x+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-6/3x-3+1-5/2=0

We calculate fractions


(-45x^2)/12x^2+96x/12x^2+(-24x)/12x^2-3+1=0

We add all the numbers together, and all the variables

(-45x^2)/12x^2+96x/12x^2+(-24x)/12x^2-2=0

We multiply all the terms by the denominator


(-45x^2)+96x+(-24x)-2*12x^2=0

Wy multiply elements

(-45x^2)-24x^2+96x+(-24x)=0

We get rid of parentheses

-45x^2-24x^2+96x-24x=0

We add all the numbers together, and all the variables

-69x^2+72x=0

a = -69; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-69)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-69}=\frac{-144}{-138}
=1+1/23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-69}=\frac{0}{-138}
=0
$