-8-2/5x=-3/10x+1

Solution for -8-2/5x=-3/10x+1 equation:

-8-2/5x=-3/10x+1

We move all terms to the left:

-8-2/5x-(-3/10x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+1)!=0

x∈R


We get rid of parentheses

-2/5x+3/10x-1-8=0

We calculate fractions


(-20x)/50x^2+15x/50x^2-1-8=0

We add all the numbers together, and all the variables

(-20x)/50x^2+15x/50x^2-9=0

We multiply all the terms by the denominator


(-20x)+15x-9*50x^2=0

We add all the numbers together, and all the variables

15x+(-20x)-9*50x^2=0

Wy multiply elements

-450x^2+15x+(-20x)=0

We get rid of parentheses

-450x^2+15x-20x=0

We add all the numbers together, and all the variables

-450x^2-5x=0

a = -450; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-450)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-450}=\frac{0}{-900}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-450}=\frac{10}{-900}
=-1/90
$