2/x-3=5/2x+11

Solution for 2/x-3=5/2x+11 equation:

2/x-3=5/2x+11

We move all terms to the left:

2/x-3-(5/2x+11)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+11)!=0

x∈R


We get rid of parentheses

2/x-5/2x-11-3=0

We calculate fractions


4x/2x^2+(-5x)/2x^2-11-3=0

We add all the numbers together, and all the variables

4x/2x^2+(-5x)/2x^2-14=0

We multiply all the terms by the denominator


4x+(-5x)-14*2x^2=0

Wy multiply elements

-28x^2+4x+(-5x)=0

We get rid of parentheses

-28x^2+4x-5x=0

We add all the numbers together, and all the variables

-28x^2-1x=0

a = -28; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-28)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-28}=\frac{0}{-56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-28}=\frac{2}{-56}
=-1/28
$