6/x+5=72/2x-5

Solution for 6/x+5=72/2x-5 equation:

6/x+5=72/2x-5

We move all terms to the left:

6/x+5-(72/2x-5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

6/x-72/2x+5+5=0

We calculate fractions


12x/2x^2+(-72x)/2x^2+5+5=0

We add all the numbers together, and all the variables

12x/2x^2+(-72x)/2x^2+10=0

We multiply all the terms by the denominator


12x+(-72x)+10*2x^2=0

Wy multiply elements

20x^2+12x+(-72x)=0

We get rid of parentheses

20x^2+12x-72x=0

We add all the numbers together, and all the variables

20x^2-60x=0

a = 20; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·20·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*20}=\frac{120}{40}
=3
$