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

Wy multiply elements

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

We get rid of parentheses

-100x^2+10x-35x=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{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-100}=\frac{50}{-200}
=-1/4
$