3/10x-10=4/5x-5

Solution for 3/10x-10=4/5x-5 equation:

3/10x-10=4/5x-5

We move all terms to the left:

3/10x-10-(4/5x-5)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/10x-4/5x+5-10=0

We calculate fractions


15x/50x^2+(-40x)/50x^2+5-10=0

We add all the numbers together, and all the variables

15x/50x^2+(-40x)/50x^2-5=0

We multiply all the terms by the denominator


15x+(-40x)-5*50x^2=0

Wy multiply elements

-250x^2+15x+(-40x)=0

We get rid of parentheses

-250x^2+15x-40x=0

We add all the numbers together, and all the variables

-250x^2-25x=0

a = -250; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-250)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-250}=\frac{0}{-500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-250}=\frac{50}{-500}
=-1/10
$