-3/5x-6=5+5/10x

Solution for -3/5x-6=5+5/10x equation:

-3/5x-6=5+5/10x

We move all terms to the left:

-3/5x-6-(5+5/10x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/5x-(5/10x+5)-6=0

We get rid of parentheses

-3/5x-5/10x-5-6=0

We calculate fractions


(-30x)/50x^2+(-25x)/50x^2-5-6=0

We add all the numbers together, and all the variables

(-30x)/50x^2+(-25x)/50x^2-11=0

We multiply all the terms by the denominator


(-30x)+(-25x)-11*50x^2=0

Wy multiply elements

-550x^2+(-30x)+(-25x)=0

We get rid of parentheses

-550x^2-30x-25x=0

We add all the numbers together, and all the variables

-550x^2-55x=0

a = -550; b = -55; c = 0;
Δ = b2-4ac
Δ = -552-4·(-550)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-55}{2*-550}=\frac{0}{-1100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+55}{2*-550}=\frac{110}{-1100}
=-1/10
$