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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

/x-x+1/3+3/4=0

We calculate fractions


-x+()/48x+16x/48x+27x/48x=0

We add all the numbers together, and all the variables

-1x+()/48x+16x/48x+27x/48x=0

We multiply all the terms by the denominator


-1x*48x+16x+27x+()=0

We add all the numbers together, and all the variables

43x-1x*48x=0

Wy multiply elements

-48x^2+43x=0

a = -48; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-48)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-48}=\frac{-86}{-96}
=43/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-48}=\frac{0}{-96}
=0
$