x*7/2x-1/6=x+1/4

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

x*7/2x-1/6=x+1/4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x*7/2x-x-1/4-1/6=0

We calculate fractions


-x+672x/288x+(-72x)/288x+(-32x)/288x=0

We add all the numbers together, and all the variables

-1x+672x/288x+(-72x)/288x+(-32x)/288x=0

We multiply all the terms by the denominator


-1x*288x+672x+(-72x)+(-32x)=0

We add all the numbers together, and all the variables

672x-1x*288x+(-72x)+(-32x)=0

Wy multiply elements

-288x^2+672x+(-72x)+(-32x)=0

We get rid of parentheses

-288x^2+672x-72x-32x=0

We add all the numbers together, and all the variables

-288x^2+568x=0

a = -288; b = 568; c = 0;
Δ = b2-4ac
Δ = 5682-4·(-288)·0
Δ = 322624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{322624}=568$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(568)-568}{2*-288}=\frac{-1136}{-576}
=1+35/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(568)+568}{2*-288}=\frac{0}{-576}
=0
$