3/4x-1/2=-1+5/6x

Solution for 3/4x-1/2=-1+5/6x equation:

3/4x-1/2=-1+5/6x

We move all terms to the left:

3/4x-1/2-(-1+5/6x)=0


Domain of the equation: 4x!=0

x!=0/4

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

3/4x-(5/6x-1)-1/2=0

We get rid of parentheses

3/4x-5/6x+1-1/2=0

We calculate fractions


(-144x^2)/96x^2+72x/96x^2+(-80x)/96x^2+1=0

We multiply all the terms by the denominator


(-144x^2)+72x+(-80x)+1*96x^2=0

Wy multiply elements

(-144x^2)+96x^2+72x+(-80x)=0

We get rid of parentheses

-144x^2+96x^2+72x-80x=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{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-48}=\frac{16}{-96}
=-1/6
$