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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-216x^2)/192x^2+96x/192x^2+(-32x)/192x^2-1=0

We multiply all the terms by the denominator


(-216x^2)+96x+(-32x)-1*192x^2=0

Wy multiply elements

(-216x^2)-192x^2+96x+(-32x)=0

We get rid of parentheses

-216x^2-192x^2+96x-32x=0

We add all the numbers together, and all the variables

-408x^2+64x=0

a = -408; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-408)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-408}=\frac{-128}{-816}
=8/51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-408}=\frac{0}{-816}
=0
$