3/x-6+3/5x-30=11

Solution for 3/x-6+3/5x-30=11 equation:

3/x-6+3/5x-30=11

We move all terms to the left:

3/x-6+3/5x-30-(11)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/x+3/5x-47=0

We calculate fractions


15x/5x^2+3x/5x^2-47=0

We multiply all the terms by the denominator


15x+3x-47*5x^2=0

We add all the numbers together, and all the variables

18x-47*5x^2=0

Wy multiply elements

-235x^2+18x=0

a = -235; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-235)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-235}=\frac{-36}{-470}
=18/235
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-235}=\frac{0}{-470}
=0
$