6/7x=2/3x+10

Solution for 6/7x=2/3x+10 equation:

6/7x=2/3x+10

We move all terms to the left:

6/7x-(2/3x+10)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x+10)!=0

x∈R


We get rid of parentheses

6/7x-2/3x-10=0

We calculate fractions


18x/21x^2+(-14x)/21x^2-10=0

We multiply all the terms by the denominator


18x+(-14x)-10*21x^2=0

Wy multiply elements

-210x^2+18x+(-14x)=0

We get rid of parentheses

-210x^2+18x-14x=0

We add all the numbers together, and all the variables

-210x^2+4x=0

a = -210; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-210)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-210}=\frac{-8}{-420}
=2/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-210}=\frac{0}{-420}
=0
$