7/2x+5/4=2+1/6x

Solution for 7/2x+5/4=2+1/6x equation:

7/2x+5/4=2+1/6x

We move all terms to the left:

7/2x+5/4-(2+1/6x)=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

7/2x-(1/6x+2)+5/4=0

We get rid of parentheses

7/2x-1/6x-2+5/4=0

We calculate fractions


360x^2/192x^2+672x/192x^2+(-32x)/192x^2-2=0

We multiply all the terms by the denominator


360x^2+672x+(-32x)-2*192x^2=0

Wy multiply elements

360x^2-384x^2+672x+(-32x)=0

We get rid of parentheses

360x^2-384x^2+672x-32x=0

We add all the numbers together, and all the variables

-24x^2+640x=0

a = -24; b = 640; c = 0;
Δ = b2-4ac
Δ = 6402-4·(-24)·0
Δ = 409600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{409600}=640$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-640}{2*-24}=\frac{-1280}{-48}
=26+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+640}{2*-24}=\frac{0}{-48}
=0
$