10/10x=4/8x-20

Solution for 10/10x=4/8x-20 equation:

10/10x=4/8x-20

We move all terms to the left:

10/10x-(4/8x-20)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 8x-20)!=0

x∈R


We get rid of parentheses

10/10x-4/8x+20=0

We calculate fractions


80x/80x^2+(-40x)/80x^2+20=0

We multiply all the terms by the denominator


80x+(-40x)+20*80x^2=0

Wy multiply elements

1600x^2+80x+(-40x)=0

We get rid of parentheses

1600x^2+80x-40x=0

We add all the numbers together, and all the variables

1600x^2+40x=0

a = 1600; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·1600·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*1600}=\frac{-80}{3200}
=-1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*1600}=\frac{0}{3200}
=0
$