1/2x+1/4=3+7/6x

Solution for 1/2x+1/4=3+7/6x equation:

1/2x+1/4=3+7/6x

We move all terms to the left:

1/2x+1/4-(3+7/6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(7/6x+3)+1/4=0

We get rid of parentheses

1/2x-7/6x-3+1/4=0

We calculate fractions


72x^2/192x^2+96x/192x^2+(-224x)/192x^2-3=0

We multiply all the terms by the denominator


72x^2+96x+(-224x)-3*192x^2=0

Wy multiply elements

72x^2-576x^2+96x+(-224x)=0

We get rid of parentheses

72x^2-576x^2+96x-224x=0

We add all the numbers together, and all the variables

-504x^2-128x=0

a = -504; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·(-504)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*-504}=\frac{0}{-1008}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*-504}=\frac{256}{-1008}
=-16/63
$