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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


144x^2/96x^2+24x/96x^2+(-16x)/96x^2-2=0

We multiply all the terms by the denominator


144x^2+24x+(-16x)-2*96x^2=0

Wy multiply elements

144x^2-192x^2+24x+(-16x)=0

We get rid of parentheses

144x^2-192x^2+24x-16x=0

We add all the numbers together, and all the variables

-48x^2+8x=0

a = -48; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-48)·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*-48}=\frac{-16}{-96}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-48}=\frac{0}{-96}
=0
$