5/6x-2/3x=7/10

Solution for 5/6x-2/3x=7/10 equation:

5/6x-2/3x=7/10

We move all terms to the left:

5/6x-2/3x-(7/10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-2/3x-(+7/10)=0

We get rid of parentheses

5/6x-2/3x-7/10=0

We calculate fractions


(-378x^2)/180x^2+150x/180x^2+(-120x)/180x^2=0

We multiply all the terms by the denominator


(-378x^2)+150x+(-120x)=0

We get rid of parentheses

-378x^2+150x-120x=0

We add all the numbers together, and all the variables

-378x^2+30x=0

a = -378; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-378)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-378}=\frac{-60}{-756}
=5/63
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-378}=\frac{0}{-756}
=0
$