5/6x=2+7/10x

Solution for 5/6x=2+7/10x equation:

5/6x=2+7/10x

We move all terms to the left:

5/6x-(2+7/10x)=0


Domain of the equation: 6x!=0

x!=0/6

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

5/6x-(7/10x+2)=0

We get rid of parentheses

5/6x-7/10x-2=0

We calculate fractions


50x/60x^2+(-42x)/60x^2-2=0

We multiply all the terms by the denominator


50x+(-42x)-2*60x^2=0

Wy multiply elements

-120x^2+50x+(-42x)=0

We get rid of parentheses

-120x^2+50x-42x=0

We add all the numbers together, and all the variables

-120x^2+8x=0

a = -120; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-120)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-120}=\frac{-16}{-240}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-120}=\frac{0}{-240}
=0
$