(9/x+1)-5/2=8/3x+3

Solution for (9/x+1)-5/2=8/3x+3 equation:

(9/x+1)-5/2=8/3x+3

We move all terms to the left:

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


Domain of the equation: x+1)!=0

x∈R



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

x∈R


We get rid of parentheses

9/x-8/3x+1-3-5/2=0

We calculate fractions


(-45x^2)/12x^2+108x/12x^2+(-32x)/12x^2+1-3=0

We add all the numbers together, and all the variables

(-45x^2)/12x^2+108x/12x^2+(-32x)/12x^2-2=0

We multiply all the terms by the denominator


(-45x^2)+108x+(-32x)-2*12x^2=0

Wy multiply elements

(-45x^2)-24x^2+108x+(-32x)=0

We get rid of parentheses

-45x^2-24x^2+108x-32x=0

We add all the numbers together, and all the variables

-69x^2+76x=0

a = -69; b = 76; c = 0;
Δ = b2-4ac
Δ = 762-4·(-69)·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-76}{2*-69}=\frac{-152}{-138}
=1+7/69
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+76}{2*-69}=\frac{0}{-138}
=0
$