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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


216x^2/192x^2+96x/192x^2+(-224x)/192x^2-2=0

We multiply all the terms by the denominator


216x^2+96x+(-224x)-2*192x^2=0

Wy multiply elements

216x^2-384x^2+96x+(-224x)=0

We get rid of parentheses

216x^2-384x^2+96x-224x=0

We add all the numbers together, and all the variables

-168x^2-128x=0

a = -168; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·(-168)·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*-168}=\frac{0}{-336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*-168}=\frac{256}{-336}
=-16/21
$