6-1/5x=8-7/10x

Solution for 6-1/5x=8-7/10x equation:

6-1/5x=8-7/10x

We move all terms to the left:

6-1/5x-(8-7/10x)=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

-1/5x-(-7/10x+8)+6=0

We get rid of parentheses

-1/5x+7/10x-8+6=0

We calculate fractions


(-10x)/50x^2+35x/50x^2-8+6=0

We add all the numbers together, and all the variables

(-10x)/50x^2+35x/50x^2-2=0

We multiply all the terms by the denominator


(-10x)+35x-2*50x^2=0

We add all the numbers together, and all the variables

35x+(-10x)-2*50x^2=0

Wy multiply elements

-100x^2+35x+(-10x)=0

We get rid of parentheses

-100x^2+35x-10x=0

We add all the numbers together, and all the variables

-100x^2+25x=0

a = -100; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-100)·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*-100}=\frac{-50}{-200}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-100}=\frac{0}{-200}
=0
$