1/4x+1/6x=2/3

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Solution for 1/4x+1/6x=2/3 equation: 



1/4x+1/6x=2/3

We move all terms to the left:

1/4x+1/6x-(2/3)=0



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R





Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



We add all the numbers together, and all the variables

1/4x+1/6x-(+2/3)=0

We get rid of parentheses

1/4x+1/6x-2/3=0

We calculate fractions


(-288x^2)/216x^2+54x/216x^2+36x/216x^2=0

We multiply all the terms by the denominator


(-288x^2)+54x+36x=0

We add all the numbers together, and all the variables

(-288x^2)+90x=0

We get rid of parentheses

-288x^2+90x=0

a = -288; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-288)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-288}=\frac{-180}{-576}
=5/16
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-288}=\frac{0}{-576}
=0
$

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