10/x+11=25/6x+3

Solution for 10/x+11=25/6x+3 equation:

10/x+11=25/6x+3

We move all terms to the left:

10/x+11-(25/6x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x+3)!=0

x∈R


We get rid of parentheses

10/x-25/6x-3+11=0

We calculate fractions


60x/6x^2+(-25x)/6x^2-3+11=0

We add all the numbers together, and all the variables

60x/6x^2+(-25x)/6x^2+8=0

We multiply all the terms by the denominator


60x+(-25x)+8*6x^2=0

Wy multiply elements

48x^2+60x+(-25x)=0

We get rid of parentheses

48x^2+60x-25x=0

We add all the numbers together, and all the variables

48x^2+35x=0

a = 48; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·48·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*48}=\frac{-70}{96}
=-35/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*48}=\frac{0}{96}
=0
$