6/7x+1/2+2/5x=211/70

Solution for 6/7x+1/2+2/5x=211/70 equation:

6/7x+1/2+2/5x=211/70

We move all terms to the left:

6/7x+1/2+2/5x-(211/70)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

6/7x+2/5x+1/2-(+211/70)=0

We get rid of parentheses

6/7x+2/5x+1/2-211/70=0

We calculate fractions


(-73850x^2)/9800x^2+12250x^2/9800x^2+8400x/9800x^2+3920x/9800x^2=0

We multiply all the terms by the denominator


(-73850x^2)+12250x^2+8400x+3920x=0

We add all the numbers together, and all the variables

12250x^2+(-73850x^2)+12320x=0

We get rid of parentheses

12250x^2-73850x^2+12320x=0

We add all the numbers together, and all the variables

-61600x^2+12320x=0

a = -61600; b = 12320; c = 0;
Δ = b2-4ac
Δ = 123202-4·(-61600)·0
Δ = 151782400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{151782400}=12320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12320)-12320}{2*-61600}=\frac{-24640}{-123200}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12320)+12320}{2*-61600}=\frac{0}{-123200}
=0
$