6-4/5x=8-1/10x

Solution for 6-4/5x=8-1/10x equation:

6-4/5x=8-1/10x

We move all terms to the left:

6-4/5x-(8-1/10x)=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

-4/5x-(-1/10x+8)+6=0

We get rid of parentheses

-4/5x+1/10x-8+6=0

We calculate fractions


(-40x)/50x^2+5x/50x^2-8+6=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-100x^2+5x+(-40x)=0

We get rid of parentheses

-100x^2+5x-40x=0

We add all the numbers together, and all the variables

-100x^2-35x=0

a = -100; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-100)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-100}=\frac{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-100}=\frac{70}{-200}
=-7/20
$