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

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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 $

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